They could make it so all that is known by banks is that you purchased the service. Like how Nym does it or how you can buy Mullvad credits on Amazon.
Ideally they accept Monero and do unlinkable payments but I doubt they will accept Monero. Hopefully they accept some crypto.
> you can buy Mullvad credits on Amazon
That is not the same thing.
You buy a Mullvad scratch card on Amazon and you redeem the token string.
Mullvad also offer the option to put your card number into the Mullvad website, and I'm sure many privacy conscious people would be very reluctant to do that.
Card payments these days leave far too big a trail. The bank knows, the intermediary (e.g. Stripe) knows, and the merchant (e.g. Mullvad) has to keep records for accounting/tax requirements.