As a former soldier, I, for one, would rather go into a potentially dangerous situation with body armor despite its weight than going with out because of the comfort-ability issue, I would rather live.
That is the one thing that generally bugged me was the lack of personal protection in the Trek Universe. I understand about not taking a security team to a diplomatic mission, but any mission where there is a big unknown, such as a brand-new planet, I would take the cumbersome gear.
Granted all the gear will be nullified by a writer, but at least have allusions to it or show a redshirt using them. As for the Klingons' armor, it may have started out as armor, but they are just uniforms.
I always kinda of thought as the Argo as a low-profile for low-tech worlds and there are various different level tech vehicles for each mission profile.