But if the image persists then how you can see a refresh? Simple answer - you can’t. Your brain is fooling you, just as it fools you into thinking it sees motion.
Seems you are assuming a display is some sort of perfect digital device instead of a flawed mechanical representation of reality.
If I look out of the window at a ball moving across my vision then different rods and cones are excited in my eye as the ball moves in my 'frame' of vision. My eye is stimulated by a constant stream of photons from the object in each 'persistence' period.
My brain does lots of smart magic and I 'see' an object moving. I can also do smart things like move my eyeballs or head to track which allows my brain to provide a better focused 'image' and predict the path of the object.
In actuality our eyeballs are darting about all over the place constantly to provide a composite image.... but that's another level of complexity.
Now compare this to a screen.
A backlight light is pulsed for a period dependant on base brightness setting. On a low end monitor this could be 100 times/sec, on a high end 400+
Between each pulse of light, the mechanical shutter on each pixel is subject to a voltage and then does it's best to get into the correct position in time so that the photons sent to my eye at the next flash of light are the 'correct' ones.
This cannot happen instantly for all pixels on the panel so it takes time to refresh the screen before the backlight strobes. More expensive panels and driver electronics reduce the time needed to make the change.
My eye therefore sees a number of photon snapshots it stitches together rather than a constant steam of photons, and each snapshot is also corrupted by the errors in the display depending on how quickly the LCD can respond.
Depending on alignment of my visual 'persistence' , the backlight pulse and accuracy LCD shutters vs target at the moment I get a several doses of photons blasted into my eye during each persistence period, all a little bit different from the last in a moving image.
Looking through a window and looking at a monitor are not the same thing from the perspective of stimulating the eye, the brain perceives motion but it does not have the same subtle stimulation from the constant stream of photons.
A monitor refreshing at 180Hz better replicates motion of an on screen object vs looking out of a window than a 30Hz or 60Hz monitor as it stimulates the eye in a way more consistent with reality.
I.e. with multiple smaller pulses of photons activating differing groups of rods and cones to provide the composite image rather than a few buckets of them.
This is the reason VR at 72Hz feels a lot worse and can induce more nausea than VR at 120Hz.
While the 'frames' we can 'see' may be capped quite low, the motion the eye can perceive is much higher and we naturally feel when something is wrong.
The in perceived smoothness between my old 32" 75Hz monitor and the replacement 165/180Hz screen is easily detectable in racing, close action flying games etc. Less so in FPS at least for me.
There is still blur at speed but things like signage at the track edge, the graduation between kerbs look better defined, I can read signage set back from the track that I can't at lower refresh rates though closer to the track it is still blurred as the pixel 'movement' per frame is just too high.
I've gamed at 60-75 fps for decades, sometimes < 50fps like with my initial run through Cyberpunk and I've never had an issue with it, but I have noticed differences instantly when playing games I know well on a friends PC with a high end monitor at a high refresh so I do agree with the posters who say they can feel a difference... because I can too.