I can only speak from my own experience, but I would not feel confident not bringing an amp (unless there was a specific backline) at most places we play. Part of this is we're not using IEMs yet. Some places we play have full / quality sound that could support IEMs and likely carry everything, but an awful lot do not, and when you're on tour playing new places, you never quite know what to expect.
The other issue is we play big, loud music which includes things like feedback and harmonics that can require big, loud amps... it's kinda part of the thing.
By way of example, we're doing some recordings right now using a few guitar heads and an Ox. The Ox sounds great! I could see using it live too, because it does a really convincing job at sounding like a cab with various mics. But without an active cab, realistic feedback and some stuff that goes along with playing through loud amps, just isn't possible. On this session, we're going to have to do some additional tracking with live amps.
Granted, I realize many many of you aren't in the above scenario, and solid monitors / IEMs will do the trick. But unless you're playing a specific spot on the regular that you are comfortable with the sound system - or managing your own IEMs / Sound for every show, you're gonna need something to make some noise.