One problem with bar mitts is that they limit the number hand positions. On my mt. bike I can't use the bar ends. On the road bike setup you can't use the more upright position.
Bar mitts haven't crossed my mind for months..... but OK.
Yes, bar mitts limit hand positions, no question. OTOH, it can be hard to operate STI shifters with very thick mittens.
But in the deep cold, I'll choose bar mitts and limited flexibility.