It's hard to answer you without knowing what kind of action games you like. If you enjoy mechanical challenge with mature combat systems, I feel like the modern era has given us several excellent action games:
God Hand, Vanquish, Devil May Cry, Devil May Cry 3, Ninja Gaiden (2004)..
Now you're just playing dumb. Devil May Cry released in 2001. Nobody really considers this era decline, generally speaking. The decline industry-wide happened simultaneously as it did for RPGs, unless you were utterly sheltered. Mid to late 2000s. Not a single
average action game (or RPG) in sight in that time, let alone a good one, with some very rare exceptions. Unless you're secretly a fan of Oblivion or Bioshock, which are not-ARPGs.
What's your basis for considering a game "modern", because it's 3D? I doubt anyone considers Doom "modern". Considering games from 2001 modern is a strange phenomenon. When someone refers to the modern era, why would it not entail the era where the video game industry started to smash Hollywood and all other forms of electronic entertainment with the likes of Call of Duty? Where everything started to look realistic graphically and the dominance of cinematic design. Where shady business practices were ramped up to 11. Where the style and focus of pretty much every genre shifted and developers soldout en masse? The death of many beloved long-standing game series, or the rise of them in ultra-commercialised form. And so on.
There is pre-decline spanning the early 2000s and before (old school principles) and post-decline (modern, as detailed above), everything else is irrelevant. There was such a shift in all things videogaming, almost none of it good. That style of design, all bullshit business practices etc is still contemporary now, hence still modern. Although I probably have to state once again that things are slowly looking up in the past few years.
I feel like what is happening in your case is a kind of bitter cognitive dissonance. You are so entrenched in this view that even though many genres have indeed turned to utter crap (RTS, RPG, FPS to a large extent) other genres have been having a bit of a renaissance or at the very least still provided good titles in reasonable quantities.
Ah, so we've gone from "the decline is exclusive to RPGs" to now include shooters and RTS. Progress, at least.
Sports games are excellent right now, as are racing simulations. Mechanical action games, as stated, are quite refined, and the SHMUP, in its bullet hell incarnation, is at the peak of game design in terms of enemy placement and difficulty to unfairness ratio (extremely difficult, completely fair)
SHMUP? As in on-rails blasting? Yeah, this was never really a great genre. It's be like Pacman clones still living on as its own genre today. Fun? Good? Enjoyable? Sure, but never a genre brimming with potential like RPGs.
Racing simulations? More simulations than games. Ultra-realism faggotry. Of course they're doing well.
Sports games, well arcade racers have declined, and if Rocket League is any indication there's still some strong decline in sports. Overall I'm not big on the genre, yet I'd agree it's not something that has seen as much decline as other genres and there's perfectly logical explanations for it, such as it being a genre heavily based in realism and pre-defined well established game rules that absolutely everyone understands (e.g football).
Action games are/were pure shit in the dark ages of the Xbawks 360 era. Now they're slightly better but still decline. Again, with some exceptions.
It's hard to answer you without knowing what kind of action games you like.
I either really like or just enjoy enough to occasionally dabble with nearly every genre and their respective subgenres.
I mostly only exclude MMO, JRPGs with overbearing art styles (so 70% of them), walking sims and games that aren't really games. Note: classic adventure games are typically still games just about, as they included puzzles and investigative gameplay.
I may have just bashed SHMUPs for instance, but I played one just the other day.