Great American? Crockett partied while his family went hungry. Lost the election and went to Texas. Indications are he was deserting the Alamo when he was killed.
Unfamiliar with your first allegation. Reference please.
As far as your last allegation, accounts vary, but I believe the preponderance of evidence is that he went down fighting. AFAIK, only one Mexican officer made such allegations.
BTW, one reason I think Davy was a great American is why he lost the election.
He vociferously opposed the immoral, illegal and unconstitutional removal of Indians from their treaty lands east of the Mississippi.
In a frontier district, this wasn’t very popular. But it was IMO highly honorable, especially since he knew it would probably lose him the election.