I have to 100% agree with OP. I recently revisited some old games via Raspberry Pi emulation and it's just not the same. With technology these days you would think we could somehow revisit our classics and play them the way they were meant to be played (CRTs etc.) Although a lot of people don't care, having proper response is crucial, to me, to have a great experience. It's just not the same how pressing a button doesn't immediately result in an action like it used to. It's not going to stop me from playing any game, but is definitely a small factor in enjoyment.
I just hope next gen they try to lower control lag via wired, as it seems PS4 Wireless mode is the only one that does it right at the moment at the expense of battery life.
Also someone pointed out Samurai Shodown's input lag. I played it all weekend and it was the very first thing I noticed even with Game Mode on... This was on Xbox btw, with the game coming out in a month, I hope something can be done as Tekken also uses UE and has tried to reduce the lag. Guilty Gear is the gold standard as I recall with 3-4 frames.
Developers can't address our TVs, but Sony/Microsoft CAN address the control hardware.