I mean, sure, but I and probably 99% of other folks have a credit card set up to autorenew. This is a security problem, but not a very serious one.
The price should just be the present value of the annual fee cash flows.
Turns out that sum of PV($X in 1 year) + PV($X in 2 years) + … converges even though the series is infinite. Look up “perpetual bonds”.
The value of $10 paid annually forever is probably $200-500 depending on [things].
Source: I work in a bank but I’m also shit at finance so take this with a large grain of salt.
Though the traditional way would just be finding a registrar which can direct debit (e.g. CSC Global or MarkMonitor) or setting up a trust account for someone to manage it for you. Or just power of attorney plus escrowed account.
Then the question is whether we want cryptocurrencies or not (I don't).