I found this, which I consider quite solid advice:
http://stackoverflow.com/a/21722205/466498
Basically, he advises against using Composer on a production server. (I think he made a mistake talking about a “deployment machine” where I think “development machine” was what was meant, reading the rest of the message).
I’m not constrained by shared hosting, but I don’t want any service to “automagically” install things on a production server before testing it on my development machine.