Why do some holidays have "Eves" but not others?

Why isn’t today “Thanksgiving Eve”? Why not Easter Eve? Or Independence Day Eve?

Is it just Cristmas and New Year’s that have Eves? Are there others?

Christmas has the “preparation for Santa” and at New Year’s, the parties all have sto start before midnight so that the revelers will be sloshed by the time the date changes.

I suspect that you will find "eve"s whenever there is a celebration that kicks off (in any way) before the official date. (Hallowe’en–All Hallow’s Eve–is now bigger than the day to which it was the eve in those countries where All Saint’s Day is no longer a serious religious holiday.)

Wasn’t Christmas (or Saturnalia, or whichever began the gift-giving, partying thing) originally a three day celebration - Xmas Eve, Xmas Day, Boxing Day?

New Year’s Eve is naturally because the celebration has to begin the day before the changeover, though.

It may be because the church calendar follows the Jewish custom that the day begins at sundown. That’s why there are Midnight masses on December 24.

By contrast, for Easter, the Gospels tell that the disciples went to the tomb early in the morning and found it empty, so the Easter traditions may focus more on the begining of the day.

No, Boxing Day was a 19th century creation.

Correct - most of them are holidays with long established religious roots, in contrast to e.g. Thanksgiving.

In Sweden we have Easter Eve.