But just for a moment, let's say that Wilson is a little bit smarter than we take him for. Let's say, also, that Wilson was a Teddy Roosevelt in sheep's clothing.
Let's see if that helps explain things. It doesn't make sense for America to waste resources crusading into Europe in 1914, '15, or '16, like Charles Evans Hughes wanted to, since it would be better to let the Europeans bleed for a little while. If you're interested in strengthening America, then it's probably best to join in when you have hints that Germany is weakened, but not quite so weak that the peace would more or less be a British-French peace.
This also explains why Wilson could so massively flip-flop from "He kept us out of the war" to "a crusade to make the world safe for democracy" in one year; and, not to mention, go through three totally divergent foreign policy approaches in his secretaries of state, William Jennings Bryan, Robert Lansing, and finally, Bainbridge Colby. It's only Colby who can really be called "Wilsonian," as we mean it nowadays.
There's something serendipitous about the time that the Americans showed up in France; we were just late enough in the war that it didn't cost us a whole lot, and just early enough that we were able to really include ourselves in the peacemaking. More than that, we had made the Allies financially dependent on us.
What a perfect situation. Now, naturally, we would like for Europe to continue to be fragmented, so we don't want Germany to become a French puppet. Lo, self-determination looks like a fine excuse. And by presenting the impression of an "Anglo-American" peace to the French, we drive a wedge between London and Paris. And since we didn't allow the French to completely dismember Germany as an industrial power as they wanted to, which might have totally prevented the country from its recovery under Stresemann and later Hitler, we laid the seeds for either a new European balance of power (which was what Stresemann wanted) that worked to America's benefit or the Second World War, which unequivocally ended Britain and France, and Germany as great powers.
The only failure, it seems was allowing the Soviets to spring up. But remember, Wilson was a key mover in sending the expeditionary force to Murmansk. And it was really the Republicans in the 1920s who abandoned the affair, after Wilson was incapacitated.