Thinking out loud here, but I don’t think this is as real a risk as it may first appear to be. In most cases I think the owners of the road would rightfully make sure their property is used per their rules. But if we had a society-wise protest (like in Hong Kong), the general laws/rules would be ignored anyways and not much changes between the public and private scenarios.
The problem with today’s protests in America is that it is mostly extreme views from a fringe segment of society that are represented, rather than moderate/balanced views. I’m not sure why so much attention is given to these protests, because it seems like a really poor signal to use for any purpose. Others who may disagree have no accessible avenue to represent counterpoints due to a lack of psychological safety, sometimes a lack of physical safety, and due to a lack of time (especially if you have a family). My gut feeling is that if it became harder to hold those protests (due to public versus private infrastructure), we wouldn’t complain much as a society.
Lastly, the legal right to assembly is regulated in America, by time manner and place regulations. Protesters often ignore those laws and block infrastructure they have no right to block, ignoring the law. I think they should be arrested by force then, but my point is I don’t know that the public versus private angle but will matter to those crowds anyways if other laws don’t matter either.