Greater Dandenong City Council does not issue resident parking permits. I have followed this up with council officers some time ago, and I know, understand and agree with the reasons why this council does not issue resident parking permits.
In my opinion, if Council did issue resident parking permits, some of the negative impacts would be:
Residents would use on-street parking more. Some residents that currently park on their own land would choose to use their garage as extra storage space and park their car on the street full-time. This would mean less availability of on-street parking for residents and visitors.
Council would need to strictly monitor permits to make sure the permits are used properly. Permits would need to be visible on the dashboard and show the car license plate number. A resident when applying for a permit, would need to prove their residential address and also prove ownership of the licence plate number. This verification would need to be redone yearly due to changed addresses and license plate numbers. Without this strict verification, permits would be abused by being lent, hired out, or on-sold to train commuters or others.
So, while issuing one permit for yourself would solve your problem, making permits available to all residents (or even just residents in your vicinity) would create many more problems in terms of on-street parking capacity.