If he did the treaty would have fallen apart when the Euros protested and Wilson would have gotten nothing. That was the reason he couldn't have compromised. In hindsight to you the French security treaty is the most important thing, but Americans and even Wilson had different opinions. A peacetime Frano-British-US alliance wouldn't have lasted and pretty much fell apart anyway over reparations and the Ruhr issue. The only thing even making such a temporary alliance possible was fighting Germany without that boogey man they had too many divergent interests to actually have a binding treaty.Wilson was an idiot, though; that's the thing. A more rational US President would have agreed to the Lodge Reservations. Likely even Thomas Marshall had Wilson's stroke killed him in late 1919.
Whether the Lodge Reservations would have neutered the Versailles Treaty is really besides the point; the French Security Treaty is much more important here. I'd easily accept the LR in exchange for getting the FST ratified. A peacetime Franco-Anglo-American alliance would be quite formidable!