Totally. Life and death, liberty and detention....they have that power, backed up by the state, over all of us. The skill set needed and the type of mental makeup required aren't in all of us, and they should be compensated well to get the best. Certainly more than bank tellers and card dealers.
They still shouldn't take issue with being filmed. They should desire it in fact. For their own protection.
Yes, of course they should. They are also human, so that might impact how they are doing their jobs, even if it shouldn't.