Because if they find out your registration was fraudulent a day later, how are they supposed to dig your anonymous ballot out from the barrel?

It's for the same reason most insurance policies have a waiting period. To prevent the most low-hanging fruit of fraud.

I've actually seen this happen in big cities where they have same-day popup registration tents in the middle of skid row, signing up random homeless people who don't even have stable addresses. No verification, nothing, we'll worry about that later here take a ballot. I'm sure everything was on the up-and-up there.