Why - read but not update ops fail in case of lacking space in tempdb database?
(Converting my comment to an answer. I don't know if this is definitive, but it makes sense to me. If you can prove it wrong, let me know in the comments.)

The row versions aren't actually required to complete a write operation; they're only required by readers that come along and need those versions of the rows. If they need them.

If tempdb runs out of space during version generation, while that's not okay, it may end up working out if no readers need those versions. A read operation would only fail if it needs a version of a row that isn't in tempdb.

Furthermore, any write operation is considered more important than a SELECT, for obvious reasons (same idea as when the Deadlock Monitor figures out which process to kill if there's a deadlock), so it's preferable to fail a SELECT if possible.