Edit: obligatory explanation (thanks mods for squaring me away)…
What you see via the UI isn’t “all that exists”. Unlike Reddit, where everything is a black box, there are a lot more eyeballs who can see “under the hood”. Any instance admin, proper or rogue, gets a ton of information that users won’t normally see. The attached example demonstrates that while users will only see upvote/downvote tallies, admins can see who actually performed those actions.
Edit: To clarify, not just YOUR instance admin gets this info. This is ANY instance admin across the Fediverse.
Still you can easily and quickly check if a user has voted on a particular post. While your method makes the tracking process quite a bit slower, it doesn’t make it unrealistic. There just aren’t that many users and posts as is the case with passwords. Still 100% better than the current approach, I hope this gets implemented.