(1) TR made his promise not to seek another term on Election Night
after it was clear he had defeated Parker. So it's not like he said it to reassure voters in the 1904 election.
(2) He didn't say he wouldn't run again
in 19
08--he said (or seemed to say) he wouldn't run again--period. "On the 4th of March next I shall have served three and a half years, and that three and a half years constitutes my first term. The wise custom which limits the President to two terms regards the substance and not the form, and under no circumstances will I be a candidate for or accept another nomination."
https://library.cqpress.com/cqresearcher/document.php?id=cqresrre1927031900 In 1912 his supporters argued that (in the words of
The Outlook) "When a man says at breakfast in the morning, 'No, thank you, I will not take any more coffee,” it does not mean that he will not take any more coffee to-morrow morning, or next week, or next month, or next year'" This analogy was much discussed (and usually derided):
(3) Obviously, he didn't have to make any such statement. If he hadn't, he could have run again in 1908 and said he was seeking a "second elective term"... Obviously some people would be unhappy and say that the substance of the no-third-term tradition was being violated, but TR would get the Republican nomination and beat Bryan without much difficulty. (If his running mate wouldn't be Fairbanks it would be another conservative like Taft's OTL running mate James Sherman. The Republican leaders could swallow a moderately progressive presidential candidate if that seemed essential to victory, but they always insisted on balancing him with a conservative running mare.)
(4) TR, as in his first two terms, would probably succeed in balancing the progressive and conservative wings of the Republican party--certainly better than Taft. The Democrats would still probably make some gains in 1910-- even with as skilled a leader as TR, the Republicans are going to show some wear and tear after controlling the White House for fourteen years--but probably not nearly as much as in OTL. I don't think he will run again in 1912--that would be too blatant a violation of
any conception of the third term tradition--but it is not clear to me who his successor as GOP candidate will be. As in 1908, Taft would be an obvious choice--except that Chief Justice Fuller died in 1910, and Taft might be appointed to his position. TR admired Elihu Root, but was no doubt aware that as a conservative Wall Street lawyer, Root would be unpopular in the West and Midwest. Hughes was another possibility, but TR never seems to have had a very high opinion of him...