For the same reason most fire trucks in the USA have plastered on the back "Remain at least 300 feet behind vehicle".
... "Emergency vehicles" such as fire trucks and police vehicles respond to Emergencies. Emergencies are by definition unsafe.
So you could "follow" (from very far behind) -- but it's implied often times that individuals are following closer than permitted in order to provoke a response, or simply without discretion to the publics safety.
Because police engage in dangerous situations by their very nature. Following them around will likely put followers in unsafe situations as well. Following them and engaging in antagonistic dialog will detract from their ability to do their job. Imagine trying to asses an area before entering a building to deal with a domestic (likely one of the most dangerous things an officer deals with on a regular basis) when someone is antagonizing you.
Filming should be legal. If there is an interaction occurring, police should have the expectation of being filmed. They should be required to wear body cameras. They should be accountable. But what this guy was doing seems to slip over the line into obstruction.
I feel like in this case, if this person is in fact a "cop chaser", the issue is that they follow the police around and essentially harass them. It's one thing to be off minding your own business, it's another to make a hobby or career out of going out of your way to swear at cops and try to record them responding in a negative manner. YMMV.
Because police routinely go right into the middle of situations that are already unsafe. That's their job. Additional persons getting involved unnecessarily in those situations is a random factor that is unlikely to make those situations safer.
I can think of a number if situations in a number of jobs I have had were people following me around could have been dangerous (farm hand, concrete work etc).
But - in my opinion obviously - if following even someone like me around might be dangerous in certain situations then definitely I can see how it might be dangerous to follow police around?
That said, I am not saying you shouldn't be allowed to folliw police at a safe distance, at a safe speed, recording what you see etc as long as it isn't obvious that they are doing something that temporarily needs to be kept secret.
... "Emergency vehicles" such as fire trucks and police vehicles respond to Emergencies. Emergencies are by definition unsafe.
So you could "follow" (from very far behind) -- but it's implied often times that individuals are following closer than permitted in order to provoke a response, or simply without discretion to the publics safety.