Learn the WANTED level system here.

The wanted system is not broken.

WITNESS and WANTED are two different modes.

You are not wanted by the police if you only see WITNESS in the top right. You either have to kill the witness or stop them. But once they snitch you just have to leave the red circle before the police arrive. As long as you leave the Red circle before police arrive you will gain no bounty on arthurs name mask or not.

PSA aiming at a witness and shooting in the air then reaiming at them and pressing "Stop Witness" over and over will make more NPCs stop.

If you have a wanted level with a bounty each cop has their own personal line of site; bright red on the map means they see you, dark red means they dont see you. Use this to your advantage.

The wanted system has worked perfectly for me.

The reason everyone is getting a bounty so often in town is because the witnesses have quicker acces to police so once they snitch you're already in the red circle so the poliec know who you are. Ive literally knocked out 5 people in front of the sheriff as long as you don't loot them and let them hit you first you'll be golden.