So now, because of bad actors, I need to pay for the privilege of watching a website or using a service that was meant to be free? No, thanks.
I don't have a solution, but "break how the web currently works" is not one I would accept all willy nilly.
EDIT: yes, I realize we already broke the web (with Anubis, cloudflare, recaptcha etc) but I think we should resist slowly breaking it further.
First of all - I suppose it should be very cheap. So, real humans will not pay much.
Second - why do u think that websites are meant to be free? They provide some service, so its a rather strange that the internet is so free (in both senses). I think, this freeiness is allowed to greatly speed up popularization. But for me is obvious that it can demand payment for service.
And third - service owner really meant it to be free, I don't see any problems with this in my idea. It can still provide free service.