I'm surprised that Goldar, Rita, and Zedd have never tried to expose their identities to the public.
In one episode, Goldar literally appeared at Billy's house.
I think we can get to some conclusion by what's said way later in Ninja Storm, that the powers can only be destroyed/stolen when they are in Ranger form.
I think it's kind of rule that the powers will not work if the identities are known since people would like the Rangers to solve every little issue and that would be " escalating a battle ", Zordon said "you should never escalate a situation". The evil guys need the powers , to steal them they need to attack them while transformed, but they won't have powers if they break the morphing grid rules.
The evil guys could cause destruction lol they want but without stealing the powers they know that sooner or later a new group will appear to stop them.
P.S. A few people they trust knowing they are the Rangers is fine, also some liberties taken for artistic value, specially cause Zordon said people may know only if the situation is dire. (Not counting the reboot that was Lightspeed)