1. Separate violent people from society
2. Separate people who through a long pattern of behavior have proven they cant or are unwilling the follow the laws of civil society
Economic status should not be a factor
Fining a rich person is simply giving them the option to pay for a pass to do something that's supposed to be illegal.
There is a rule in my state that cars have to display license plates on both the front and rear of the car. But one of my cars has a sharp sporty front end and the licence plate bracket would be ugly. So I just eat the ticket I get once in a blue moon. Mentally it's simply my trivial token service charge for getting to have what I want.
I don't know what the fair penalty should be for that infraction, but if the goal is to ensure every vehicle displays plates on both sides because it's actually important, then it's not whatever $50 or $100 I paid maybe once, possibly twice in 20 years. Maybe the fine just needs to be a percentage of income or assets instead of an arbitrary fixed value, or maybe it needs to be some other consequence that I actually feel yet won't unfairly harm someone else more than me for the same wrongdoing. (I can afford to take lyft everywhere for instance, or just stay home even, so even losing my license would inconvenience me slightly, but could be devastating to someone else.) Or if the goal is just to collect a fine and no one cares about the plates, well then job done I guess.
But the point is I don't know if "blocking a public path" should qualify for prison exactly either, but there are other possible justifications for prison than just seperation. It may be simply a consequence that actually matters to the people whos actions you are trying to regulate.