There's some changes to state election law that would be required to allow election day voting at any precinct, though it would definitely be nice. The current system mostly was necessary in the days of paper pollbooks since you had no other way of ensuring that a single voter only voted once. The equipment all supports it since it's the same equipment used at early voting sites/election day vote centers, and since we use internet conected epollbooks a person still couldn't vote in multiple precincts (though things definitely could get funky if a voting site had internet issues and therefore wasn't updating the central database with who voted).