There are approximately 3000+ organized counties or county equivalents in the US. Do you think we should have 3000 representatives in the House?
You can't organize federal election by county. The population is not distributed even close to even in them. For example, Democrats in dense urban areas, for example, would simply create 100 new counties to increase their total number of representatives. Republicans in rural areas could break up their big counties with low populations into small counties with even lower population in order to increase their vote totals.
What you propose doesn't even make sense.
Election fraud through gerrymandering
“In gerrymandered election districts, the voters don’t choose their politicians - the politicians choose their voters!”
Yeah. If anything, we're under-represented. As for representation by counties, that's a straw dog. We do need less opportunity for gerrymandering. Smaller districts are needful. But still proportionate. Non-citizens should not count to pad the rolls for districting.