I did get two postdoc offers in the humanities by emailing profs whom I'd never met and asking if they were willing to sponsor me for a couple of postdoc competitions. So it's certainly possible.
That's different to asking to be someone's post-doc with no reference to applying for a post-doc fellowship to be carried out in the location of the person you are e-mailing.
Or maybe that's what the OP means?
In both cases the prof in question is still the supervisor, although supervision in the humanities for postdocs seems to be almost notional. But you're correct as the funding model in the humanities is that everyone has to find their own money, whereas there's more of a commitment from postdoc supervisors if the funding come their own research pot.