To address the "empty Concorde" problem, Boom is explicitly targeting a 50-seat business class layout with similar seat cost per mile. Filling 50 comfortable seats is an order of magnitude easier than filling 100 uncomfortable ones.
Building certain premium flights around it, not necessarily; Singapore Airlines operates a 67-seat business class on a plane from Newark to Singapore that only has business and premium economy. BA operates a 32-seat business-only flight from London City to New York via Shannon. And these are just the subsonic flights.
JAL is one of the bigger investors in this project, so it's not as if there's no interest at all.
BA1 rarely flies full. The ego is right there in the number. It’s a novelty.
SQ hasn’t operated business class only since like 2011. It has 67 business seats and 94 premium economy seats. And still probably loses money.
The one you didn’t mention was Stavenger to Houston which... only flies when oil is flying high. Because it’s not profitable otherwise.
Theoretically speaking, if the seat cost per mile is as low as advertised some airline might want to take some business class seats out and put some premium economy in. What a plane does with seating layouts is its own concern.