I really can't agree, OP. Looking at just the PS3 alone, I can't agree. Then when I factor in PC, Xbox 360, Nintendo, and the deluge of indie titles that graced us during that time period, I REALLY can't agree.
You're stating your subjective opinion as objective fact, and that's not going to harbor a real discussion. For you, there weren't a lot of games in a genre you love. For me, I got so many games in genres I love (action/adventure, rpgs, open world titles, etc, etc), and I was also introduced to genres I never thought I'd give a shit about (ie, visual novels). I was never a big multi-player gamer, so all of the fantastic single player titles like Half Life 2, Portal, GTA, inFAMOUS, Fallout, Bioshock, Demon's Souls, etc, etc, had me in bliss. I was a huge PlayStation fanboy back then, but there was also no denying how excellent Xbox LIVE was for opening up online gaming and indie developers to a wider audience. Sure, there was a lot of crap, but there was also a ton of quality titles that weren't just mega blockbusters or sequels. And we can't pretend that the sequels to some of the previous gens best games were weak either.
Subjectively, I can't argue with your perspective, because for you, those years were lacking. Objectively, though, there's a mountain of gaming that says 2004-2009 was a banner period for gaming. Developers were really coming into their own in regards to designing games in 3D, and establishing a language that has carried us forward to where we are now. There are good and bad things that come from that, but overall, the industry is moving forward, and developers are continuing to produce quality content. I highly recommend looking to indie developers for titles in genres that may now be niche. I also suggest playing more games that may not be in genres you adore. You never know when that one game will crop up that makes you a fan.
I remember I hated JRPGs back in the day, and it took Chrono Trigger to release in 1995 before I gave JRPGs a shot and became obsessed with the genre. From there, it was a hop, skip, and a jump to titles like Phoenix Wright and Dangan Ronpa, and Persona, etc, etc. Expanding your gaming palate is one of the key elements of continuing to enjoy gaming.