Personally, I think the identifier "Action Adventure" is a flawed term.
I find Action and Adventure concepts as mutually exclusive when considered as the primary driving mechanic of a game. A game can't be primarily driven by both action events (i.e.e real-time combat) and adventuring (the puzzle solving/adventure themes as discussed above). One or the other will dominate progression:
1) When a game's primary mechanism of progress is reflex based (platforming, real-time combat wins, etc.); adventure elements become secondary and act more as gate mechanisms to separate new combat arenas/sequences. It'd simply be an action game that contains adventure-like elements. Frankly, this is why I feel the Metroidvania & Dungeon-Crawler categories aren't adventure games.
2) When a game's primary mechanism of progress is the story-driven puzzle solving as discussed in the above posts, action sequences in that game simply become (mostly) unnecessary interruptions to progressing through the puzzle solving story of the game.
In fact, these type of reflex-based action sequences are often complaint points of adventure games; especially when they outright prevent progress just because the player doesn't have the reflexive skill to complete the action portion. It's this exact reason that some adventure game developers included the option to skip such action sequences in their games (though there is sometimes a penalty for not at least attempting the action sequence). For example, in the original EGA version of Space Quest 1, there is an unskippable arcade sequence of riding a skimmer (personal hovercraft type vehicle) across a boulder filled desert. Some people really struggled to complete this portion of the game; effectively halting progress half way through a game otherwise driven by puzzle solving, simply because the players didn't have the action-game-level reflexes to complete the sequence. Due to complaints, Sierra released the VGA remake of SQ1 with an option to simply skip the skimmer sequence (they also introduced a method of negating the slot-machine portion).
In my opinion, most games that would be given an "action adventure" label would likely be better categorized as Metroidvania, Platformer, Shoot-em-up, etc.
Frankly, the term "Action" itself is too general of an identifier when categorizing games. We have various categories of Action games (those just mentioned) into which games can be more specifically categorized. Adding "Action" to "Adventure" and trying to categorize a game as "Action Adventure" likely ignores better, more specific categorization in a different category.
TL:DR "Action Adventure" to me is an unnecessary term trying to introduce an (overly broad) special category of gaming that simply isn't a necessary distinction compared to game categories already commonly used which themselves are more descriptive of the game type (Metroidvania, platformer, shoot em up, adventure, etc.).
I wouldn't be so hasty to condemn the term. I think it can be quite well used for a game that otherwise fulfills most of what makes a game an "adventure game"... except that in addition there's a real-time combat element (or other real-time elements requiring timing, reflexes or other kind of real-time skill). In other words, "an adventure game with some action game characteristics added on top of it". A combination of both.
What would you classify such a game as, if not "action adventure"? I mean, let's assume that it has all the hallmarks of a pure adventure game (open world, large inventory, need to find and collect items, need to use those items in a non-trivial manner eg. in puzzles to advance) with the exception that there's also a real-time combat element to it?
The term "action" could also likewise be used with other genres, like "action RPG" (which would describe a type of RPG that uses real-time combat requiring skill and reflexes, rather than a turn-based take-your-time combat system).
This, basically. It covers metroidvania, zelda-like, and stealth games.
Although I am definitely fine with, as Drd2k9 suggests, using more specific subgenres as tags instead. The one thing we should not be doing is giving such games two separate "action" and "adventure" tags, as is the case now.
Firstly, I can't think of a game off the top of my head that fits this description and wouldn't be better categorized by a more descriptive genre than "Action Adventure." (But that is kinda beside the point on a hypothetical question.)
Perhaps it's wrong of me, but I'd argue that it's rare for a gamer to be looking for a game that combines heavy aspects of both of these genres. Most players wanting to play an adventure type game aren't wanting heavy action involvement in the gameplay. Similarly, players seeking a primarily action oriented game don't typically appreciate heavy thinking/puzzle solving to be a major part of the game's progress.
The reason for this comes down to the type of gaming. Players typically are seeking a specific gaming experience when choosing a game to play. They don't want the desired experience arbitrarily/randomly interrupted just because a developer was trying to force together two significantly different styles of gaming. Due to this, there simply aren't many games that contain significant quantity of action elements into a true adventure driven game, or vice versa.
But if such a game did exist, I'd categorize it based on the PRIMARY method of progress. If the adventuring is designed to be the primary limiter of progress and there is simply some occasional combat, I'd describe it as an adventure game. If the combat was designed to be the primary limiter of progress and there were simply some adventure parts, I'd categorize it as a primarily combat (action) game.
As I've already mentioned (and is also stated in the above linked wikipedia article), "Action Adventure" is a very broad category; where games that would qualify can better be described by another genre that is more descriptive of actual gameplay.
If a game as you've described above exists with equal emphasis on both gameplay styles, it could be best described as a 1st/3rd Person Combat Adventure; but I doubt that the game would sell or be reviewed very well due the drastic gap in the two forced gameplay styles.
True, but there's little to no confusion on what "Action" means when describing RPG's. Even still, there's could be a more descriptive method of describing such a game: Turn-based Combat RPG, Real-time Combat RPG, Dungeon Crawler (as many Dungeon Crawler's have real-time combat and RPG elements), etc.
This is just another example of my original assertion that "action" is too general of a term for describing gameplay (even when not trying to attribute it to adventure games).
TL:DR
To develop a game that truly balanced action and adventure styles equally in limiting progression would be to force a gamer to completely (and consistently) shift from one style of play to another simply to make continued progress. This is contrary to the way most gamers want to play games. They chose a game based on the type of experience they want, and they don't often appreciate being forced into a different style.
Games like LoZ:OoT and Super Metroid are generally classified as "action-adventure". How would you classify them? ("Metroidvania" is a rather informal term.)
...and wouldn't be better categorized by a more descriptive genre than "Action Adventure."
Neither of these games (or any in their series) fit the description of a primarily adventure type game that includes action elements. Both of these games are just the opposite. They are primarily action games that happen to have some minor puzzles or minor inventory item management, but there's rarely (if any) challenge in deciphering what the inventory item is used for in the game.
I personally don't consider either of these game series as having enough adventure driven elements to to even be classified as adventure games at all. In my opinion, the problem with an "Action Adventure" label in these cases is that the "adventure" part is the problem, not the "action" part.
As far as a specific genre/category for these two games: Super Metroid is by default a Metroidvania game; it's a game from one of the two series that the genre's name itself literally comes from.
While it may also be somewhat broad/informal, "Metroidvania" is still more descriptive than "Action Adventure" and is thus a better descriptor and the one which would be more appropriately used between these two labels.
The Zelda series are very much a similar style game to the Metroid series with new items mostly granting the ability to open new doors/paths. The biggest difference (at least in the first game of each series) is in camera perspective. After those two games, camera perspectives may have changed, but the driving mechanic of gameplay remains Metroidvania style with movement and combat being the primary progression mechanisms. Where inventory is concerned in the Zelda series, it's mostly there to open/allow new doors/paths, not as an internal challenge of figuring out what the inventory items themselves are even for. Sometimes simply having them in inventory is usually enough to get the necessary effect. Even the trading sequences in Zelda games aren't overly challenging in figuring what stuff is for, it's typically very obvious for the player if not outright told to them.
To put it simply, Both OOT and Super Metroid fit into the Metroidvania classification better than the Adventure classification. "Metroidvania" is more descriptive than "Action Adventure" and thus a more appropriate label for these games.