Vote-by-mail, or any system where there is no voting booth with official overseer, lacks anonymity.
Voters need the right of keeping their vote secret, but that is not enough. If voters can show who they voted for, they can be intimidated or otherwise induced into voting for someone in particular. They can of course say who they voted for, but they cannot be allowed to prove it to someone else.
That is what the voting booth is for. With generalized vote-by-mail, we would see much more vote buying and small-scale intimidation such as “vote for my stepbrother if you want to keep your job”.
I am surprised that so few people make that connection when the issue arises.