does not have wither skeleton egg

This isn't a bug, there isn't a snow golem egg either.
This is more like a 'feature' or something like that.

The standard skeleton egg works as a wither skeleton egg in the Nether.

Ah, lol, stupid... I thought you meant 'wither boss'.
Nope, that's true, I think it's because wither skeleton and skeleton have the same entity ID. Pretty annoying indeed.

This is like the Zombies example, You can randomly get a villager zombie with the regular zombie egg, maybe you can get randomly wither skeleton with the regular one.

There is not supposed to be one.