It’s hard to believe membership wouldn’t do just that - but when I moved out of SA many years ago and went to transfer my membership, I found that it didn’t cover any vehicle I drove, it covered my car - like my car was the member? The point here is, I didn’t transfer my membership out of the RAA - I just changed my address to my new ‘interstate address’ - there is no need to reside in the state you have membership to receive roadside assistance and the other (claimed) benefits, but of course any local benefits might be too far away to take advantage of … that’s not why I’m a member anyway. It may be that some of the premium offerings in other states now cover you for any vehicle - I’ve never bothered to revisit and verify.
You are not alone - it seems I’ve had somewhat of a rant a number of times on this forum and suggested a CHOICE review 
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not to mention HERE, HERE, HERE, HERE, and HERE … oh dear …
I will say, I had roadside assistance recently and it was timely, excellent and friendly, however I do stand by my views on the ‘non-roadside-assistance’ aspects of these organisations …
