As long as the ballots are counted on election day, I don't see anything wrong with it.
Unlike absentee voting, which I believe should be illegal except in certain excemptional situations.
That seems like a wonderful way to disenfranchise college students, for example, who usually go to school far enough away from home (4+ hours) that it isn't feasible for them to return home to vote. If Election Day were in April, maybe, but with Election Day in November, there's not enough time to register locally.Registration should be automatic anyways.
Mind you, I'm talking about what should be, not what squares with the US Constitution, which was the original question here.
The argument against postal voting is a secrecy one, of course.
At least over here, the most typical postal voter is an elderly couple filling in the papers together at the dinner table.
Military on a short-term mission abroad that began before the early voting period, aye.
Otherwise, no. Those outside the country for a lengthy period should not be allowed to vote at all. Within the country, they should day vote - or early vote, if that is impossible - at their base. Obviously, the military is another area where the secrecy of the ballot is very much endangered currently.
The main exceptions would be people falling to sick to get their ass to the polling booth at short notice, and people living dozens of miles from a polling station.