Actually, and this is key, there _are_ reasons why deposits might not

be able to use PaymentRequests. Payments happen even when
wallets/computers are offline.

I don't understand this point. It's the sender that is parsing the PaymentRequest and following the instructions. By definition the sender must be online. A computer that is switched off cannot sign a transaction at all.

If you have negotiated HD wallet details, you can use a new address
every time, as mentioned.

Yes, and an extension to BIP 70 to allow for this (or stealth addresses or whatever) has been discussed several times.

This thread started by proposing (I think) an expiry time for addresses. BIP70 satisfies this use case, I think we all agree on that. Now for cases where someone can't use BIP70 for whatever reason, or it's suboptimal, absolutely we should design extensions to fix that.