If they didn't list party affiliation on ballots, people would instead vote based on what? The names they like most? That's about how informed some voters are, unfortunately. It takes effort to get informed, and the entities that should inform them, often fail to do so.
That said, it is somewhat sad that the informed citizen is a more rare voter than they used to be. The ballot in my state was so long that I had to make a cheat sheet to avoid having to memorize all of the names. I suspect that for non-partisan offices, a lot of people did just vote for names they like. If elections weren't so costly, it might be objectively better to hold local, state, and federal elections on different days, so that people who show up to vote for a president or a governor don't just mark the rest of their ballot without knowing who they're voting for.
These are all senators, though, so it can be assumed that they were mostly elected by people who at least had heard of them.
Honestly, that's the best idea I've heard in a long time.