Which is why we have "1st Amendment Zones", endless debates on the 2nd Amendment, the NSA violating the 4th Amendment with impunity, and American citizens being denied their 5th Amendment rights via armed drone.
And the wikipedia summary is pretty good: "Unlawful assembly is a legal term to describe a group of people with the mutual intent of deliberate disturbance of the peace. If the group are about to start the act of disturbance, it is termed a rout; if the disturbance is commenced, it is then termed a riot."
So in other words, if the police allege you were there not to protest but to start a riot, they don't actually need to wait for the riot to start. You are probably thinking "man, it seems like the police can abuse that law just by always claiming the crowd looked like they were going to become violent". And you are correct, but that's the way it is.
I don't think "eager" is the right word here -- I hardly believe anyone, cop or citizen, is eager to escalate a situation where nobody is going to win. It's bad mojo for both sides if it continues.