the sun is ~400 times wider than the moon, but it is also ~400 times farther away. because of the symmetry, the lunar umbra that falls on the face of the earth is (for all intents and purposes) exactly wide enough to cover the face of the sun. but that needn't be the case.*
q "is this just some bizarre cosmic chance?"
a "yes. and it's not static. it only appears that way at this particular point of time in our history. the moon is moving away from the earth. about 600 million years from now, it will have moved far enough away that there will no longer be total solar eclipses on earth."
*if unsourced statements on the interwebs are to be believed anyway.
i asked bythos for a song & he gave me recovering the satellites. well played!
(this was one of the favorites adam sang last week)