Am I remembering wrong that the new FT mechanic requires the calling official to stay table side? So if you are T and call a shooting foul (or foul in bonus), you're not going to switch?

You are remembering correctly.

So that would be one reason why it's not always "important" to switch on all fouls in 2-man. :)

True. This is the new mechanic beginning this year.
However, in 2-man, most shooting fouls are called by the Lead, not the Trail, so this doesn't happen very often, and doesn't really undercut the point that switching is of the utmost importance in that system.