You also have issues of deanonymization if you only get a couple of ballots in via one method. In Maryland, for example, they're supposed to encourage at least 100 random people to use the accessible ballot marker per precinct for this reason.
It's not reasonable to tell people "too bad," fly back to the US as much as 3 times per year. They pay taxes and are subject to US law even though they're overseas, so they get to vote.
Ballot management becomes error prone. My county alone has 25 ballots due to the different combinations of state house, senate, Federal house, municipalities, and _all_ the special districts. (4 members to the board of directors of the Anytown West Memorial District, a.k.a. cemetery, because they had a property tax assessment when they built the thing in 1950)