I agree 100% for the reasons others have detailed above. Certainly not something I would ever advocate being done.
I also strongly agree with RA-Aus thinking on why they have stopped forwarding bills to members. If anything, Andy has probably understated the cost to RA-Aus of doing forwarding invoices. I would put the cost as more than $20 to receive the invoice, register its receipt, look up the members details, re-address and forward on the invoice.
There is no way I can think of that RA-Aus can be sued for the actions or inactions of its members in the same way that members cannot be sued for actions or inactions of RA-Aus - these are different legal identities and RA-Aus in this case is a third party to a debt between a member in their own right and an airport operator.
I do advocate paying landing fees. It would be nice if all aircraft operators recognised the low impact of a 600kg aircraft compared with much heavier GA aircraft but airport operators are free to set their fees. We can accept their fee structure and land at their airport or reject and go somewhere else. No different to any other normal business situation.
If you land at an airport you have formed a contract. The airport operator offers their runway facility for a price (consideration) and you accept their offer. The moment the rubber hits the tarmac you have a debt. But, it is a commercial matter between the parties to that contract and RA-Aus has no business being involved in any way. It is up to airport operators to develop cost-efficient billing and collection systems as is the case for every business in the world.
The airport operator can't blame RA-Aus because the airport operator has ineffective commercial systems. As an example, Wyong Shire Council decided that it wanted to manage, inter alia, collection of airport fees at YWVA. They had one of their employees attend the airport and note the registration details of each aircraft as it landed. Hardly an efficient system but that is up to the WSC and other airport operators as to how they manage their commercial relationships and not RA-Aus.
There are a great number of good reasons, many listed above, why privacy must be respected.