Just a data point. My team manages about 15 different brands with a couple hundred million annual page views and we pay north of $100K a year for fonts and believe that to be a good value for the money. The difference between a good Monotype font and a free or cheap font is worlds different when your concerned with a brand looking as good as can be. The cheaper fonts sometimes have odd space in them that make letter spacing or line-height changes look horrible.
We haven't. Although we do plenty of testing in general. We don't view it as a ROI driver, just an element of a strong brand. Which is much more subjective.
Surely just aesthetic pleasure is worth something? Shall we all live, work and play in brutalist utilitarian buildings unless it can be demonstrated that there are better results from something else?
I used to work at eharmony. One of the biggest complaints we had from users was that paid users were still shown ads. The users hated it, but the analytics showed that we made more money with the ads than without the ads so to hell with the users' experience on the site, we had better results with the ads.