> The reasoning for such extremely strict geographic restrictions, I am unsure of, but surely it would also argue against mail-in ballots (and I would assume smartphone voting).
One reason is a holdover from the days when the eligible voter roles were physically printed on reams of paper to be lined through in pen as each eligible voter 'checked in' to be given a ballot.
If your system for preventing double voting is by a line drawn in pen across a voters entry in a paper printout, then you have to allocate voters to one, and only one, voting location (because you can't 'line through' in pen multiple geographically disperse paper printouts containing the same name quickly enough to avoid double voting risks).
> Side question: How are people temporarily living in distant areas from their registered county (working, attending school, etc) able to vote?
This is the purpose of the absentee ballot system. If you know you are "away" on election day, you apply for an absentee ballot and vote that way. Most of the recent "early vote" system has simply been an expansion of allowing voters to vote "absentee" by having them show up at the city/county offices before election day, fill out an "absentee" form (with less stringent requirements for proof of being "away"), get a ballot, vote, and drop it in the count box.