No, there is no practical limit that we know of yet to what would be best, there is however a practical limit to what we can capture and display.
In tests with airforce pilots, subjects were able to identify a plane from being shown a frame for only 1/220th of a second.1 They eye is able to pull information out of extremely short periods of time, but unfortunately our eyes are also very good at concealing lack of information (which is actually why video works in the first place), so it is extremely hard (possibly impossible) to determine the actual point at which we wouldn't benefit from more information.
Either way, it is almost certainly upward of the current 1/600 mark and often theorized to be beyond the 1/1000 mark. The problem comes not from how much information we present, but that we don't have enough information to present.
Generally videos are normally not played back faster than 48 frames per second at the fastest and video games normally don't go beyond actually displaying 120 or so. This is due to a lack of being able to store sufficient data and stream it in an efficient enough manner to display in an affordable manner.
Instead, to make things appear more smoothly, the TV interpolates additional frames to fill the gaps. It looks at where one frame is and where the next frame will be and generates frames in-between to smooth it out. The problem is, not all motion is perfectly smooth and interpolation isn't a perfect process. The result is that unnatural artifacts appear in the video which we can detect and end up being unsettling and eventually start causing more harm to the persistence of vision than the extra frames help.
This is why, when you move in to higher refresh rates it is sometimes better to use a lower setting without the interpolation. Video is about simulating reality for your eyes. In reality, there is no refresh rate, any time your eyes chose to process, they get whatever is there at the time. Thus, higher and higher frame rates will more closely emulate reality as long as the information is actually based around reality rather than something invented by electronics on the fly.
Eventually, we may exceed the "refresh rate" of the eye, but as of yet, we don't definitively know what that is and are pretty certain we haven't hit it yet.