I studied Digital Multimedia in college and the topic you are talking about is a bit more complicated than you seem to think it is.
The idea that people do "do not see more than 60FPS" is actually a fact (the actual frame rate humans cannot perceive is slightly lower than that, but 60FPS is nice round number), but you seem to be confusing "seeing more than 60FPS" with "recognizing 60FPS".
When we say people cannot see higher than 60FPS, we are saying there are frames flashing by so fast in the video that the human mind cannot register the data fast enough in individual frames and the information is lost. This was tested and proven in a well-known experiment. Full black frames (static pictures of nothing but black) were inserted into a video of full white frames. People were asked to watch the video and identify when the full black frames appeared. At a framerate somewhere in the 50s, all participants were unable to accurately identify where the black frames were in the video--they appeared and disappeared so fast that the human mind did not register them among the sea of white frames. So, yes, it is an established fact that humans cannot see more than 60 frames per second. There is no physically possible way with the limitations of the human body to read data on a screen fast enough to register information from one solid frame when the frame shows at a rate faster than 60FPS--there needs to be some kind of coherence or context for the frame to actually register as part of a set of frames viewed together.
That said, you are confusing seeing 60FPS with recognizing 60FPS, which are two different things. While humans cannot distinguish data from individual frames at 60FPS, if we placed two videos side by side and played them at different framerates, of course you can tell there is a difference--the difference is happening often enough that our brains can register it and tell us. But here is the thing, there is ANOTHER well known experiment that tells us we actually do not recognize the difference between the framerates compared to each other at different times. Recognizing the framerate difference and identifying the framerate difference are two different things. Just like before, if we put two videos side by side and asked a person to tell us which was playing at a slower framerate, we can usually expect a correct answer--humans can perceive a difference in framerates with direct comparisons. But, if we change up the experiment and show the videos at different times while not side by side, humans cannot accurate tell which video is playing at a faster or slower pace--we know there is a difference, but we do not know what the difference is without the other video being present to directly compare. In other words, without direct side-by-side comparison, we cannot tell if different framerates are faster or slower after certain speeds, we can only recognize them as different.
All of that said, when game developers make animations for video games, they develop those animations at a specific frame rate, usually 30FPS or 60FPS. So, no matter what you do, you cannot actually make that framerate faster than the developers made the animation. There is "interpolation" technology out there that "increases framerates", but all that really does is insert static image copies in between frames. Basically, instead of having 1 static frame showing for 1 second, interpolation copies that frame 9 times and speeds up how fast the frames show, so now you have 10 identical frames showing over the duration of 1 second. All that is doing is inserting more visual data into the video without changing the physical difference--you still get the same, unchanged image playing over 1 second. Although it is important to note that our brains recognize the difference between seeing 1 static over 1 second compared to seeing 10 static images over 1 one second. While it is possible to interpolate frames into an animation between keyframes using advanced software that dynamically redraws frames (this is how we get HD remakes of video games), this is a process that cannot be done in real time as we play the game. So, yeah, if the game was developed at 30FPS, you are not getting better graphics by interpolating frame copies, you are just making your computer much work harder to create a change that you recognize as different.
