I am not a crit racer per se but have done them. I race on tubulars tires for the reasons CDR pointed out. My wife had a front tubular blowout in a time trial on a descent on a curve and stayed up. I had a rear tubular blowout at Carson velodrome on the 45 degree banking and stayed up and just rode the bike to the apron.
I like the corner of tubulars and the feel. I would train on them but i do not like the hassle of flats and carrying an extra tire but I have friends that ride tubulars all the time.
OP, IMO, your best crit wheelset is the one you do not want to use - American Classic tubeless. Tubeless technology with tire sealant will offer better flat protection, lower rolling resistance (not tube losses) and they are round.
One thing I do not like about tubular tires is that they often are a little bumpy when installed i.e. not round. Some tires are worse than others.