And that is not even getting into the fact that private businesses' speech are constantly regulated by law.

Will private businesses get to ignore laws that say they need warning labels on certain products? I am sure there is alot of products that could sell more if those products were thought of as less dangerous. How about laws requiring the listing of ingredients on certain food products? I am sure some private companies would like some unhealthy foods to be thought of as more healthy and have unhealthy ingredients be unknown to the public.

I just don't see how it could be legal to impose these regulations on private businesses if they supposedly have free speech. If private businesses have free speech, how can they be regulated at all?