Your first bullet point is OK. The last two are dumb. I could reducto ad absurdum 'em, but why bother?
Saying that about a governor of Georgia or Arkansas before Carter or Clinton would have been dumb. However, the posts of governor of Mass, and mayor of NYC are perceived as important jobs. But, you're right, the most important fact is that no pro-abortion Republican has ever been elected president. And the "yeah but he's popular and he can win, who cares if he's not really a conservative, so let's nominate him" attitude failed miserably with Gerald Fords and Bob Dole.