I just tried this experiment. As far as I could reach, the coin did not disappear from the bottom up UNLESS I allowed the table to actually obstruct my view of the coin. Similarly to how the RE model says that the curve of the earth obstructs view of the sun and makes it disappear, if you hold your eyes low enough compared to the edge of the table, the bottom of the coin is cut off.
This is not a good representation of flat earth however. On FE, your viewpoint is positioned ABOVE the ground, which is why you can see so far. On the table, in order to make the coin disappear you have to have almost no real view of the table at all. In fact, you pretty much just see the corner! I don't think flat earth is supposed to have corners (at least not in that sense lol). You could probably replicate that viewpoint of the sun on FE if you were standing inside of a trench, but not if you were standing on flat ground.
Yes, obstruction of view. :)
When the table starts to obstruct your view it's because of the visual convergence of what is above the horizon line with what is below.
This convergence starts to happen before the vanishing point.
The table example is not perfect of course but it's an experiment to replicate what happens when something moves towards and beyond the
vanishing point on the horizon.
Your experiment never demonstrated the vanishing point.
Dave Weiss demonstrated how it works with his kitchen counter in the video I shared in the other thread, but he would need a much longer counter to demonstrate it better since he used the mountains as the vanishing point horizon line with the sun overhead.
If he had kept going further with a lonnng countertop he could have demonstrated the sun meeting with the counter top at vanishing point.
Dave's "sun" would converge with the counter top in the far distance. The bottom part of the "sun" (ball on the string above the counter) would visually disappear from the bottom up until the whole thing disappeared. It would look like it went "down behind the counter" even though in reality it stayed the same height above the counter. It's just perspective.

If you strung a ball on those lines above the tracks and moved it along at the same height above the tracks the ball would eventually look like it was getting cut off on the bottom as it converged with the horizon shortly before it disappeared altogether.
In real life the ball would stay at the same height moving along the lines above the tracks. Yet it would look like it the ball went down the further away it got. Then it would start to disappear from the bottom up.

So we are replicating what happens when an object moves towards vanishing point on the table. Not as good as the ball overhead but it still works.
Objects that move beyond the vanishing point can no longer be seen.
What happens as the quarter reaches closer to vanishing point?
It starts to get visually cut off from the bottom.
So you could say "the table starts to obstruct your view" or you could say what is above and below the table is starting to visually converge prior to vanishing point.
Imagine these boxes keep moving forward at the same height across a flat plane. Would they all crash into each other? No. Would it look like they started to converge? Yes. When they move away far enough the ones above the horizon line would disappear from the bottom up and the ones below would disappear from the top down.

Anyway, for the experiment the view of the table has to be split in half at eye level.
The horizon line is always at eye level. If you sit down at the beach and then you stand up, what happens to the horizon line? It moves down to remain at eye level.
The table can be "like" the horizon line for our experiment if we put our eye down at the level of the table so our view is cut in half.
No it's not a horizon line in the distance like at the beach.
We're making a fake horizon line right up close for our experiment to show convergence before the vanishing point.
As the coin moves beyond the horizon line into the distance it is cut off more and more from the bottom up until it is all gone from view.
That's how the vanishing point perspective works.
You can even do this with your laptop. Put the bottom at eye level and lay your finger on it. Now move your finger into the distance. It starts to disappear from the bottom up.
Visual convergence before vanishing point.