According to this: https://www.youtube.com/watch?v=BzB5xtGGsTc First/business class seats are where the airlines make all of their money, so Concord would be economically viable today.
So the airline don't need economy class to make profit, they need them to create economies of scale that bring down their cost for the high margin customers.
It only makes sense if you could attract new business class customers, who would take the faster trip but wouldn't take the slower one at all.