Try it, use a mixer for your bitcoins and sell them on some exchange. Lots of exchanges blacklist bitcoins from mixers.
Then don't do business with people who treat bitcoin as non-fungible.
What if you have billions of page loads?
You don't have to generate a new address for each page load. Just have a "Donation here!" link; whoever wants to donate will click it. Definitely not billions, not even hundreds of thousands.
I haven't seen any website that shows a new Bitcoin address on each reload, which confirms to me it's not feasible.
I've seen it once, and it was for donations specifically. Can't remember the github.io page. Doesn't BTCPay Server give you a new address each time? Why don't you use that?