Just thinking off the top of my head here:
What if SPV wallets were exempt from the fee? Only full nodes would pay other full nodes when initially sync'ing the blockchain. Then as long as you keep your full node running for a long period of time, you'll eventually make back the cost you paid to sync initially. This at least incentives full node operators to keep their node running for as long as possible once started.
This still imposes a worse UX on casual users who want full node security, but don't want to run a server 24/7 (or perhaps simply aren't aware that they have to). These users will watch their balance wither away each time they open their wallet, but it would be very difficult to explain to them why that is happening. It would just be frustrating and confusing.
Also, what happens when a user runs Bitcoin-QT for the first time after downloading it to try it out? They wouldn't be able to sync the blockchain. Even if the wallet has a balance, how would the wallet be able to see that it has UTXO's without the ability to sync with the network for free?