Lunch-counter operators might have preferred the racisl status quo, but there would always be the temptation to want to bring in customers from that other half of town. Why would any business owner who's not a fanatic want to sell to only half the town...
Capitalism is generally subversive of authoritarian rule.
Because the whites had more money and they would leave if blacks came in.
Walter E Williams gave a good description of why Jim Crow does not make economic sense and goes against the principle of free markets. One of his best when substituting for Rush.