Don't forget that before the Civil Rights Act of 1964, Southern cities such as Atlanta and New Orleans segregated their restaurants by law. For example, Section 369 of the Birmingham, Alabama Racial Segregation Ordinances contained the following clause:

It shall be unlawful to conduct a restaurant or other place for the serving of food in the city, at which white and colored people are served in the same room, unless such white and colored persons are effectually separated by a solid partition extending from the floor upward to a distance of seven feet or higher, and unless a separate entrance from the street is provided for each compartment.

So, far from being a matter of economic pressure, serving a black person in a white restaurant put you in violation of the law.

Of course, most jurisdictions in the South did not have formal Jim Crow laws related to restaurants, but in those cases segregation was enforced through custom, and backed by violence. Before the Civil Rights Movement, few blacks would have had the courage - or recklessness - to test these rules. The few examples I'm aware of involve black soldiers during World War II, most of whom were beaten - several veterans recalled being chased out of restaurants with a baseball bat - or manhandled by Military Police.

So in many ways your question is moot, since the regime of terror that existed in the segregated South made this kind of behavior unthinkable.

Note as well that most of these rules also applied to the North - most restaurants in New York City in the early 1960s discriminated against black customers - and black travellers required the assistance the Green Book to find the very few restaurants and hotels that would offer them service, regardless of which part of the US they found themselves.