Voting has eligibility requirements (citizenship, felony status depending on jurisdiction of offense) and registering someone in error could induce them to vote while inelligible, which is a serious offense.
Automatic tax filing might be nice for easy situations, but there's lots of things the IRS doesn't know and can't realistically know. Like how much capital improvements did you do on your house, and maybe even how much did you pay for your house ... whenever the IRS doesn't know the cost basis, they helpfully assume it is zero and send you a big tax bill... Still for w-2 + 1099s with cost basis reported, it could be easier.
The “system” knows who can vote, even if there might not be a unified system currently to automatically validate that.
Same with taxes. These things can be automatically reported at the time of purchase.
Eh, not really. In my previous house, I redid the master bath twice (because the first contractor did a bad job). They both qualified to increase my cost basis when they were done, but the first time no longer qualified after the second... That's theoretically trackable through some seriously invasive purchase recording, but realistically, not so much.
Citizenship is also trickier than it sounds. There's no full and complete register of US citizens to compare with. Better to have someone declare they are, and jail them if they vote and it turns out they aren't.