Also Frankie believed that it was Michael who tried to have him killed, remember when the Rosato Brother came up behind him and said, “Michael Corleone Says Hello”.
The question is, did they intentionally stop short of killing Pentageli, knowing then he would turn against Michael.
Frankie didn’t die in the bar because the cop walking a beat came through the front door.
I believe that the other family wanted to torture Frankie with the final thought before his death that the head of his own family had turned on him.