Parking regulations are governed by the DOT, the permit is issued by the DOT, therefore as long as the DOT rules are being followed I don’t see what the issue is.
It’s in everyones best interest for a Hatzala member to have his vehicle close by at all times. (Imagine if he had to run two blocks to get in his car and then do CPR.) So to answer your question- it can be used when not on calls.
As far as family/ friends using the permit and members who never go on calls- you may have a point there.