>>30819358They did have a global empire, but the political situation was really weird for them at the time.
For one, their king was devolving into some kind of dementia, something of the sort that made him much less capable. A weak executive meant the greater role of power went to Parliament, and at the time, that body of government officials were extremely loathe to actually wage the war. That's why they only sent some shit expeditionary forces, didn't press whenever they had openings, etc. The war kept becoming more unpopular in the chambers, year after year as expenses rose.
It was a weird time for them. If they were headed by a strong king that was firm in empire, they probably could've done it, yeah. But they didn't have the willingness to really just crush it. It was a lot like Vietnam, in that respect, for both the French and Americans.