That's not complicated -- just post each vote in a different box (paper can be different colours) and count them separately. OK it may take a day or two to find out who your local parish councillor is. Whoopee.
You probably start to get fuzzy about your state rep/senator. And are pretty much clueless about the county Sheriff, Board of Selectmen, and Register of Deeds.
In practice, a lot of the positions lower down on the list are running unopposed or have been in their position and seemed to have done fine for a while. Of course, this being Massachusetts, a lot of these seats are pretty much Democrat locks anyway.
We tend to have 5 or 6 layers of government too so I don’t see the problem there.
I have no issue with European countries sovereign decisions, but when Europeans project their ideas on Americans I take great offense.
Reminds me of the line from some American tv show where one character says "I don't vote, I just write down Jesus," and another says "we count that as a Republican vote."
https://www.joe.co.uk/politics/voter-writes-wnk-all-over-bal...
[0] https://www.google.com/amp/s/amp.cnn.com/cnn/2019/07/26/poli...
I went to watch a count for the local elections in May in the UK (I was a candidate)
The papers were counted in front of me and dozens of other people from the various parties. I could see each one going into each pile of ten, each pile of ten being bundled as a pile of 100 and put into a basket, the ambiguous ones (blank, voting for multiple candidates, writing "WANK" next to all candidates but one (which had "NOT WANK" written next to it), went into a separate pile.
At the end of the counting the returning officer went through the ambiguous ones with the candidate or agent and explained if he would accept it or not.
This doesn't take long - it scales, and is fully repeatable by completely different people if needed. The problems that seem to occur are not in the count, but in the returning officers (who tend to be doddery old men) writing the wrong result down, and for some reason this result is final, but that's the same whatever the counting method.