Nixon winner, GHWB winner, Taft winner, Ike winner, Lincoln winner, Johnson winner. Dukakis loser. Carter loser. Dewey loser. Stevensen loser.
Not sure how you label GHWB “winner” and Carter “loser” — both were one-term presidents defeated by governors who went on to two terms. Or how Johnson is a “winner” when he won election once and dropped out early in the primaries next time out.
Nixon, GHWB and Johnson had been Vice President, generally considered an executive office. William H. Taft had served in the cabinet (Robert Taft was a loser). Ike was a general like most presidents in the late 19th century. I will give you Lincoln, the only superior ex-legislative candidate.
Dukakis, Carter and Dewey lost to other governors. Stevenson lost to a five star general. In other words, of all your examples, only Lincoln was a valid example of your point.