You are right!!

I went and checked a warrant certificate that I have and you can in fact exercise warrants (but cannot trade the stock including the exercise warrants) before the end of the hold period.

Having said that, I would consider it "dirty pool" for a company to force the exercise of warrants before the end of the hold period. For example a company to offer a PP at $.25 with warrants attached at $.35 and then 30 das or so later come back and say "Thanks for investing your $25k for 100,000 shares in us. By the way since the SP jumped you need to give us another $35k within 30 days NOW or your warrants will expire ... and by the way you still can't trade them for 3 months."

Likely that company would never be able to do a PP again

Most people who participate in PPs will sell the underlying shares as soon as they can assuming the SP is up and hold the warrants or use the proceeds o exercise the warrants. Rarely does an investor exercise warrants out of pocket.