There is fundamentally no difference between a mail-in ballot and a ballot you drop at an arbitrary box somewhere.
(Splitting hairs here but) this isn't true: in some countries, but not all.
In some countries ID is an optional document you only need to acquire if you want to drive, vote or travel internationally.
how then should voters who are not physically present in their voting district cast their votes?
If you want people temporarily out of their district to vote, then in district X you could have a box for district Y, put paper ballots in, and send the sealed box to Y to be counted. The important thing is that the vote is cast in person by the right voter and put immediately into the box.
(hint: the answer is mail-in ballots)