I hope you find some way to still enjoy them
The solution is clearly PC gaming!
I am not sure I am capable of understanding mentality of some people in this thread. PS4K does not invalidate your gaming investment. If anything, iterative consoles make the most expensive thing in gaming, i.e. games, last longer, as you will have full backward compatibility ala Steam on PC (I sure hope so). Plus there is a good chance that most accessories will work cross consoles so all those fight sticks, wheels, controllers, etc... will work if one gets PS4K or PS5.
I have a decent gaming PC but it's already outdated even though i have a nice video card. I don't tear my hair out because someone can run Witcher 3 10-20 FPS more then me as long as I have decent enough experience. I can play Witcher 3 at 30 FPS at 1080p with a GTX 750 and can play it at 4K and 60 FPS with GTX 1080. You don't see people lamenting that those bastards at AMD and Nvidia are upgrading their video cards. Hell, if anything, people are bitching that they are not upgrading fast enough and everybody is pissed off at Intel for their CPU upgrades or at AMD for not having a decent product on the market.
Who the fuck cares that someone can run a game better then you if you dont feel like upgrading? You bet your ass that developers will not want to drop 50-60 million user base of PS4 (by the time Neo comes out) in order to capitalize on PS4 Neo. Yes, graphics will look better but you bet that your next COD, Ass Creed, Horizon, Whatever will run just fine on PS4. For Japanese games, you will still be able to play new Naruto/Guilty Gear/Whatever when PS5 comes out on PS4 still.