The mis-understanding here is that there is one election. In the US we have 3000+ county elections run/managed/under the direction of an elected county election

The mis-understanding here is that there is one election. In the US we have 3000+ county elections run/managed/under the direction of an elected county election commissioner (actual title may vary by jurisdiction). For state and federal positions and issues counts roll up to the state and higher levels, but all elections are local. There may be reasons for several counties to do common things, like standardize on voting systems across a whole state, but even that is really at the discretion of the county election commission. "...but I image many registered voters think they can just walk into any polling place on election day." I'm not sure why anyone would think that, it has never been the case. Typically, at least where I live, I get a card in the mail a few months before the election telling me exactly where my polling place is and how to get an absentee ballot if I need one.