I don’t trust Generals with political ambitions. Right answer.
Exactly—a serving General should NEVER answer yes to a question about his political ambitions. Whatever his real ambitions, Petraeus did the smart thing here (of course).
Jackson, imho, was an excellent president who, among other things, saw to it that the US debt was paid off entirely, and told both the banking interests AND the Supreme Court to go to hell. Pretty fine record, I'd say. And he, as the 'Hero of New Orleans' had known political ambitions from 1817 onward.
Grant, sadly, was a disingenuous man who believed that almost everyone he dealt with in DC was honest. He must go down as a very poor president. He was largely apolitical during his service, and I believe (can't prove) that he was drafted by a group of hardcore Republicans who knew that he could be manipulated.
Even if he were interested, it would be a distraction and he must never let it out until the war is over...
The Soldiers come FIRST.