What if President William McKinley had never been assassinated?

[StateBoiler]

I just listened to a podcast on the 1900 election. McKinley was talked into running again in 1900, so even though he would've been eligible to run in 1904, he would've likely passed.

Think Teddy would've at least ran for the Republican nomination in 1904. However, I don't think he gets it due to antipathy to him was high. The reason he became VP? A New York Republican powerbroker hated him and wanted New York Gov. Teddy Roosevelt out of New York politics. Teddy of course thought the VP job was a dead-end and wanted nothing to deal with it, but this powerbroker worked the Convention hard and got everyone onboard, including Teddy. Throw in that national party chair Mark Hanna thought little of Teddy telling McKinley at the start "your job is to live the next 4 years". Teddy would've been a strong candidate among the grassroots but if these machine smoke-filled backrooms live up to their reputation, Teddy should not have become the nominee in 1904 after McKinley served his 2nd term and they would have instead as a stop Teddy candidate backed...who knows who.

In the event he did however, that means he'd probably served from 1905-1913. And if he was as popular as he was when he left office, it means his political heir is the one that handles the growing conflict in Europe in the runup to the 1916 election, not Woodrow Wilson. I see no way Wilson ever becomes president without McKinley's assassination.