It's so you can't share a multi-day pass.

They don't really care who you are. They do care that one multi day pass stays with one person. Making sure the same thumbprint is used every time the pass is used accomplishes that; somehow registering ID might, too (but then they need to either print it on the pass, or have a database of pass serial # to ID, in parallel with their fingerprint database).

An interesting option might be to do ID one day, thumbprint the next. But I guess they're smart enough to require the choice on the first use, and then not allow it to be changed.