Well if France did not exist now things would have been easier.
If Britain did not exist you would have one less ally.
All countries hold relative importance.
If Britain did not exist, we'd have one less ally. We still could have done the job in Iraq, though with higher casualties, and perhaps a greater alliance with Australia, which has contributed greatly. In the absence of a Britain, US would have no ally close to Olde Europe, and might be in a greater conflict. Perhaps the US would then have to look elsewhere for a closest ally.