ake Deus Ex: it's mediocre in the Action department, but strong in the Adventure and RPG ones, and an excellent Action-Adventure RPG overall. Fallout 4, by comparison, is okay in the Action department, but sucks at both Adventure and RPG characteristics.
Now you got to ask yourself a question: why all these hybrids suck in one or two departments? Because these genres do not mix, just like oil and water.
Take Deus Ex: gunplay there plainly sucks, at least in the first half of the game. Why? If we make gunplay strong from the start the need for RPG mechanics will fall off. People will just shoot their way to the end, plain and simple. Fagout 4 has better gunplay, but superficial RPG mechanics. If we make RPG mechanics there more pronounced the game will become too easy, or more over the top with HP bloat or enemy numbers.
You can't make "Action-adventure RPG" that excels at all the three components. One should make a room for another, leading to mongrels of the game which are mediocre all the way around or accent one aspect over another. In Xenus 2, aiming through the sights is an actual perk that you need to choose - the thing that you have in normal shooters by default! Stalker has excellent gunplay and no stats or skills whatsoever; if we add some of these we will have to sacrifice some of the gunplay mechanics available to a player from the start. Dark Messiah has great combat, but RPG mechanics there are just simple way of locking away options from you.
To speak of Deus Ex again, it finds more or less perfect balance and this is why this game is valued so much. But truth be told, while I love Deus Ex, it is saved by excellent worldbuilding, atmosphere, characters, story, brilliant level-design and the sheer amount of options to progress available; the combat itself is not the strongest point of the game by any meaning. Deus Ex is the sum of its parts, if we remove all of the above, making a new game using the same mechanics, but with some amateur writing, bad level design and boring setting, the game will surely flop.
I disagree with your premise on Deus Ex's combat, the gunplay doesn't "suck" because RPG elements are involved, but merely because those relevant skills weren't correctly balanced. It's a failure of execution, not concept. In fact, I've recently argued and still hold that DX's approach is, in principle, the perfect mix of Action and RPG, as it capitalises on both the player's natural skills for perception and precision and, at the same time, offloads variables which cannot be adequately represented on the input device, such as recoil and sway, to the character sheet.
In concrete terms, DX's variation range from Untrained to Master was too large. The starting level at Untrained was simply too imprecise, and by the time you level up your relevant skills and install enough mods on your weapons to reach a manageable setup, you've already gotten used to play
around head-to-head combat. At the opposite end of the spectrum, DX4 implements the same core concept (even if the skills layout has changed), but it went too far in minimising the skills' impact on performance. The starting levels, with no praxis invested in the weapons handling "augs", is okay, but the increments are too subtle, you should get some slightly more dramatic results towards the high end when upping those skills.
As a sidenote, the original DX's gunplay is also unsatisfying due to the limited nature of most enemies' combat AI. It's not really relevant to our discussion on RPG mechanics, but it is a significant factor in the negative perception of the game's combat that you need to bear in mind.
Coming back to my point, my ideal implementation of RPG skills in action gunplay would be somewhere in between the original DX and Mankind Divided, start with the latter's baseline, but provide more significant upgrades in handling. It takes care and iteration, but that's the price of quality.
As to your larger argument, an Action-Adventure RPG doesn't need to
excel at being all three of those things separately, it needs to excel at being an Action-Adventure RPG: a game that comprehensively provides a framework where both the player's and the character's skills are working together in a consistent and harmonious way. It's a tough job, but certainly a realistic one, and between Deus Ex and nü-Deus Ex, you've got a pretty solid formula to experiment with. Why doesn't that happen more often? Lack of developer vision and/or budget priorities, pick your poison depending on how charitable you're inclined to be.