sure except for all the reasons cash doesn’t work for this

How would it be feasible for Anna's Archive to accept cash?

That's why most shadow libraries are funded with cash.

who do you hand the cash to in order to fund a website?

Sending cash via snail mail to buy stuff online exists. While Anna's archive does not support it, it certainly exists.

This is also forbidden by several post offices. In my country it's against the law to send money by mail.

Ok, but now you're not comparing bitcoin to cash but rather to cash+mail, which has many more tracking opportunities.

What about Monero?