Yes if you use 60 FPS then your slowest exposure time can not be slower then 1:60 second to be able to capture 60 frames every second.
And yes that is 2 X as fast as 30 FPS would do, and yes if a dashcam are allowed to it will drop to a 1:30 second exposure time.
So yes 60 FPS / 1:60 sec footage will have less motion blur than 30 FPS / 1:30 sec footage, but unless you are right there and that would matter, well it dont matter CUZ you will still have a ton of motion blur
Ideally we would like the minimum exposure speed to be 1:500 second or faster,,,,,, and that is still slow, if you use that on a camera, and hope to be able to get a good photo at the race car as it zip past you, well you will be surprised, 1:500 are only fast enough for human generated speeds like walking and maybe running.
at least that is what i remember from Photography class in school way back decades ago.
I once tested 2 similar cameras side by side, only difference was 60 FPS and 30 FPS, it was extremely rare the 60 FPS camera got a plate capture and the 30 FPS one did not, CUZ even if its 30 FPS, most of the time due to lighting conditions it will still use a much higher exposure, and chance are the 60 FPS camera will use the same faster one, say like 1:1000 second or even faster.
I did not look at sharpness back then, but yes at the minimum exposure time there would have been a difference.