Yes and no. It depends who's paying. For the most part leisure travelers aren't going to pay for anything other that basic economy. The basic economy experiment bears out that thesis: legacy airlines wanted passengers to pay more than LCC fares they had to compete with -- so they created an ostensibly painful and unattractive product in BE to encourage people to pay a tiny amount more for anything. Ultimately nobody did, and they felt they had to remove those restrictions -- and indeed most basic economy restrictions have been since lifted. The whole experiment ultimately cost airlines hundreds of millions of dollars.

Flight aggregators actually switched to providing more of this comfort information (especially Google Flights) specifically because of BE but it wasn't enough to save BE.

Business is paid for by businesses, and premium economy is paid for by, uh, cheap businesses. I think PE was brought in so in times of austerity businesses could avoid negative press associated with buying business-class airfare but still wanted to provide their employees a modicum of comfort so they could hit the ground running off the back of their flights.

LCCs are interesting, because I would argue they support my case: people won't pay more than the bare minimum fare for a flight. They may pay small amounts for comfort upgrades but the butt in seat is a commodity. Hence, legacy carriers who try and cover their costs of 50% less density in coach are going to get their lunch eaten by LCCs who don't as the pricing disparity grows larger.