Your take on history has nothing to do with what actually happened, either before or after the Boycott. The country eventually changed a bit culturally, and Park's reputation within liberal circles has undergone hagiographic reformation into a civil rights hero. Deservedly, in my opinion. But the white population of 1952 Montgomery Alabama was not by any stretch of the imagination "close to the tipping point" of racial equality or any form of voluntary desegregation. Most people were angry as hell, and Parks was not treated with any leniency whatsoever. As the controversy continued, the ranks of the countermovement known as the White Citizen's Council more than doubled. Over the course of the next year, violence intensified and there were at least six bombings within the city aimed at the protestors. Riots spurred by Parks' arrest left even other American cities, notably New Orleans, in flames. It wasn't just Parks who wound up in jail, more than 800 community organizers were indicted and submitted themselves for arrest. The Black community of Montgomery, of course, was in a different situation, but even among Black Alabamans, there was much dispute about the best course of action, and it took extraordinary talent and perserverance for ED Nixon, Jo Ann Robinson, Martin Luther King Jr, Ralph Abernathy and many others to keep the Boycott together long enough for the Supreme Court to step in and force the city of Montgomery to cave.
I think you've invented a storybook history based on what you want to believe - your parents' generation weren't really that racist, Blacks were always going to be "granted" rights eventually no matter what they did, and all it took was a few rousing speeches at the Lincoln Memorial to get the whole country singing Kumbayah and embracing a multiracial future. But that isn't what happened, nor could our present situation of rising racial animus and recriminatory violence possibly have been derived from such a lah-dee-dah past.
I realize you are likely uninterested in cracking your own paradigm, but if anyone else here is interested in learning more about Parks, the Boycott, and Browder v Gale, I highly recommend J. Mills Thornton's 2002 book, Dividing Lines, about a third of which is dedicated to exploring the situation in Montgomery (he also covers Selma and Birminghsm, equally well). Jo Ann Robinson's memoir (she effectively launched the Boycott by widely distributing the news of Parks' arrest) is well worth a read.