That's what it took. Legislatures would have laughed them out of their chambers.
Laughted out of their chambers? 3/4 of the legislatures ratifed the 14th amendment 100 years BEFORE King came to power. Try again.
And this fits into the picture how? Did this stop cities and municipalities from making unconstitutional laws which treated blacks as subhumans as did the Taney court?
No it didn't. The 14th amendment didn't mean crap. And those laws were only repealed when blacks in the south stood up to the tyrants and told them to take their laws and shove them. I know you'd like to think that blacks in the south grovelled in front of legislatures and said "please massah, may we use the good toilets and ride on the busses with the white folk, pretty please?"
But that aint the way it happened. They disobeyed.