Why is the moon exactly the right size and distance from the Earth so that it fits neatly over the sun during a solar eclipse?

Good question. Most likely coincidence. I will lurk for other answers.

It must be sheer luck.

It isn’t a perfect fit. The shadow is larger than Earth’ diameter. Not much larger, but just enough. Other than that, there is no why. It just is.

It is not an exact fit. The ratios vary significantly.
The Sun’s Angular diameter ranges from 31′27″ – 32′32″ (0.5242 to 0.5422 degrees)
The Moon’s angular diameter ranges from 29′20″ – 34′6″ (0.4889 to 0.5683 degrees)

Sometimes the Sun is larger. Sometimes the Moon is larger. Most of the time they are pretty close.

It isn’t. Because the orbit of the moon is not perfectly circular, often solar eclipses are annular, in which you can see the sun along all the moon’s edges.

We are lucky. If you wait a few hundred million years the moon will be further out and it won’t cause a total eclipse any more. Also, the Earth will be rotating slower so the days will be longer.

We just happened along at the right stage of earth/moon evolution. The average separation is still increasing, and the sun is expanding.

I mean, I can make my thumb look bigger than Mt.Everest, doesn’t make it so.

As others said above, it’s not a perfect fit.

If we lived millions of years in the past the moon would have been larger. We are lucky to live in a time when total eclipses are possible. Really, lucky to live in a time when other galaxies are visible even. Had we been around much later we may never have even known.

It is what it is.

It’s a temporary condition. In the past the moon was closer, so appeared bigger, in the future it will be further away and thus appear smaller.