That's exactly backwards from anything I've ever read about airline economics. Do you have any references to support?
https://kottke.org/17/03/the-economics-of-airline-classes
suggests that on a given BA LHR<->IAD flight, the 122 economy seats total about $107K, the 40 premium economy seats about $106K, the 48 business class seats about $322K, and the 14 first class $122K. The 14 first class seats out-rev (and out-profit) the entire economy cabin.
Citations on premium class margins don't account for the higher costs of servicing such customers (ground/airborne food and entertainment, lounges, transportation, exclusive services, etc).
While some may have a few planes with higher #s of premium seats, many fleets (especially N. American ones), are comprised of mainly economy class seats. This is obviously less true for newer airlines or those upgrading most/all of their fleets. The invention of more seating groups like premium economy (same cabin, almost no difference in service offered and cost to do so) has made one of the biggest differences to date.
Sales also extend to business and 1st class seats - this and frequent flier upgrades show that premium tickets are often sold at less than full markup.
While it's true that simply multiplying seat numbers by advertised prices is not giving the whole picture, and running lounges isn't free, the extra costs are absolutely outweighed by the far higher cost of the ticket. Full service airlines would fill the whole plane with business if they have the demand (and sometimes do).
Economy can still be profitable, of course, and there's far more passengers of that class - so airlines will obviously still run all-economy flights if the business class demand is already satisfied on a route. There's no question they're less profitable, though.
I think quite a few financial/corporate centre city pairs support a business-only flight, though even with this famously rich city pair, BA1 from london city to NY is flown on an a320! It's a difficult product to make work.
Upon further reflection I believe what the grandparent commenter was trying to say is that airlines, as a whole, get more revenue from economy pax, which is probably true for most airlines. On a route that supports a decent J component, though, they can rake in the cash.
The airlines' discriminatory marketing actions are buffeted by disparate nature of their customer base (a group of strangers who'll typically never meet again after sharing a flight) as travellers don't have enough interest in and means of organizing. Otherwise, if economy class customers boycotted en masse, that airline would suffer more than if a handful of 1st class fliers did. United Airlines' scrambling after the Dr Dao debacle was driven by desire to stem the potential financial loss, not just PR crisis.