Not just for safety - gotta look and feel the part, too
If you are paying good money for a brief jaunt into space (but then
again, the majority of people who will be able to afford these first
sub-space trips will not be poor or even middle class), I would expect
to be wearing a spacesuit. If you are going to wear shirtsleeves, you
might as well take a commercial jet and ask the pilot to do a couple of
sharp ascents and dives.