You said right modern fighters, because they are not fighters but businessman, if we are talking about old school your claim is not true since that tons of old school fighters went fight injured much worse than Liston. You said modern fighters but pre 2000s were not like that. Ali never claimed it was accidental and he said that he met the man who was working with Liston and who offered Ali some dirty tactics. Also Machen stated to and so did Zora Folley. Big deal, fought Journeyman bum half of his size with padded record. Had he fought Ali like that then yeah but since quit twice and cheated with substances I could say that he is a bully with no heart.
I hate to disappoint you but there are several instances of fighters postponing fights before the 2000s,because of conditions far lees painful then Liston's.Indeed your hero Rocky Marciano postponed a rematch with Jersey Joe Walcott because of an injured nose. Eddie Machen was lying through his teeth about being blinded by Liston. There is absolutely no evidence of his eyes being affected during his fight with Liston.It's all there on footage of the fight. Why did Machen,and Folley,say nothing about this alledged blinding for several years after their fights with Liston ? Because it never happened ! A broken jaw is a broken jaw,no natter who your opponent is.Liston showed immense courage in what was only his 8th fight.
Nope just Floyd because Floyd was peotected fighter that was exposed unlike Charles or Walcott. Johanson was the first one to deck Patterson and show that his chin was made of glass.
And yet he went in brutal fight with nose split in a half by Ezzard Charles and didn't quit unlike your hero. First it was terrible pain and second it was the blood that caused him blurry eyes. Before 2000s majority of fighters fought and won while being injured and no one was pulling excuses as much as your hero. The only one pulling so much excuses was Lomachenko for his shoulder problems when young kid Lopez exposed him...same story like Liston.
And yet Sonny Liston fought for several rounds with a broken jaw. There are several instances of fighters withdrawing from fights before the 2000s because of injuries,medical conditions etc.