Every time I've visited a site where I thought, oh that's a terrible font, it's been basically one of these reasons:
* Improper selection of default font for constrained display eg tabular
* Or the more popular "Let's create a font because we can. It's branding."
There are of course other considerations involved like the increasing diversity of rendering devices, but that doesn't make the fact that any web site font issue is nearly always the fault of the web site operator.
I can't recall any instance of "oh, that website with a great custom font is so appealing I'm going regularly and voraciously consume its content". The opposite of that is true though.