Sorry. I was not especially clear. I suspect that the "better" responsiveness of a high frame rate games is a placebo. Or, to abuse words less, is something that makes people feel good, rather than something that gets reflected in how well they play. Human response time is measured in hundreds of milliseconds, so no matter what, the game is going to be able to render multiple frames inside of the time it takes you to respond to seeing something on the screen. That doesn't mean that people can't "see" the different framerates. Just that they're not a factor when it comes to how quickly or accurately they can react to information on the screen (regardless of whether or not their brain decides, after the fact, that they would've made that shot, had they just been able to see the mob and click a button a frame earlier, or whatever.)
If you're talking about real, native frames, higher absolutely is beneficial and players do improve with it.
Whether interpolation helps improve performance in games is another matter. You have better motion clarity, but also higher latency. Latency probably matters more.
Interpolation is about looking better (smoother) and being more comfortable to play.
But if you turn it on for a game, you're taking whatever the game is doing natively to look good and run predictably, and smacking a heavy handed filter over it. I believe that this feels better to *you*, at least when you first turn it on. But I also suspect that you'd be getting a better experience, were you to just allow your eyes to get used to the lower framerate -- your brain is really good about filling in the missing information and presenting you with the illusion of fluidity. ymmv, of course. To each their own.
Interpolation is not about making a game feel better to play from a responsiveness point of view - it's about making the game look smoother.
Looking smoother "feels better" to me, because it helps alleviate motion sickness problems I frequently have with 30 FPS games.
Here's a short clip I recorded from my TV to demonstrate its interpolation. This is from a 2010 Sony TV, which is interpolating to 120 FPS. YouTube doesn't support HFR yet, so you're not going to see the full effect with a 60 FPS video.
Please keep in mind that this is filmed on my phone, so don't expect to compare still frames against each other. This is to demonstrate overall smoothness. Shooting 120Hz at 60 FPS means that individual video frames will show two TV frames blended together.
It's obviously not perfect, but it's hardly some abomination either. The main problem I have with it is that latency is bordering on unplayable on this TV when it's enabled.
With a low-latency "game mode" interpolation option, and a decade of improvements, I could see it being something that actually gets some use while gaming on my next TV. The problem is that it only seems to be Samsung with this feature right now, and I don't want another VA-type LCD.