But practically speaking an afternoon of shopping, exchanging coins for banknotes, breaking those into coins and back again will make it as untraceable as possible.

Especially since we're talking about 60 euro per year

There are no central repositories as to the location of arbitrary banknote serial numbers.

Lets assume, for the sake of argument, that a cash-paying user were to make the mistake of paying every single time to renew the same suspicious Mullvad account using cash which was always newly withdrawn from cash machines from a banking institution which meticulously tracks them and is able to report from which location they originated (maybe even the card which withdrew them!).

In that case, if Mullvad were to be compromised (or if the targeted user was such an absolute threat to humankind that Mullvad were to agree to collaborate in his or her capture), it would only be possible if Mullvad's mail receivers were to either a) actively keep track of either banknote serial number and link it to a customer, or b) be fully aware of the requirement to make a note of it only of received to renew the target account.

Anything short of that and even the perfectly traceable banknote serial number just becomes one of hundreds? thousands? deposited by Mullvad in their bank accounts — assuming they don't even use some of them as petty cash if needed.

If a user of Mullvad were to reach that level of a threat model I would argue they would be much more likely to be caught by tracking of their sent mail, in the style of Ted Kaczyński.

Yes, a neighbor may not realize they're sharing their network, however, interpreting their "next door" comment as a literal unit of proximity doesn't make your comment look as intelligent as you may think it does.