I don't think thats the point. The question is not whether or not the civil rights act improved race relations, it's whether or not the government has the authority to restrict an individuals freedom of speech on their own property when it does not cause physical harm to others or interrupt the freedoms of others. If we were only to look at the success of legislation, measured simply by its benefit to society, then for the sake of reducing crime, something that poses immediate and life threatening danger daily, we should no longer require warrants. Warrants are time and time again a hinderance to the prosecution of true criminals, dangerous individuals.
By your logic, we would look back on this unconstitutional legislation and ask "Yah, but did it get bad guys off the streets or not?"
Racism is abhorrent. Still, racism exists and the constitution is certainly an inconvenience to some peoples idea of a utopia (one with perfect social harmony). Yet, we can not restrict proprietors rights if they intend to exercise their first amendment right by restricting access to their business, just as we can exercise our right to not patronize such an establishment.