I was at NJMP last week for a DE and they were requiring convertibles to run with the top down. They wanted the flaggers to be able to see that the helmet was below the roll bar while the car was on track.
AFAIK, they were enforcing the 2" rule, but my car had a hardtop so I was not personally impacted. A friend of mine who is about 6' tall had no problem with his stock rollbar, so I assume they aren't getting too carried away.