Snarkhunter
Prince
I presume you're referring to the American War of Independence? Seriously, the redcoats were involved in more wars that just that one. A lot more in the 270~ years they were around for.
I agree with some of this. The Navy was extremely important in the creation and defence of the Empire, but so was the army, especially in somewhere like India and Africa. I can see the logic behind using a naval vessel as the English UU (especially as it is English, not British) I just think there's also a good case for the redcoat and that it's heavily supported by the gameplay elements.
Edit to Add: I think you're ignoring the impact of the British army on European history. The navy was more important to a place like north america, but its impact is much less in strictly European terms, where its major role has been to buy time. I guess in the end it depends on your viewpoint: American, the navy is more important. European, and the case for the army looks a lot stronger.
It isn't for nothing that the navy is the senior service in Britain, not the army. The army was always small & secondary to the navy, and British planners recognized that from the time of the Dutch wars on (about when leaders could no longer be both generals and admirals simultaneously due to specialization). And they proved it by what they spent their shields on for 3 centuries. Naval projection of power around Europe and the rest of the war was *enormously* influential, far more so than the few professional soldiers Britain ever bothered to field; it constrained completely the ability of the other powers to move and act as they saw fit & made sure that Britain could never really lose a war until the 20th century. (It might not win, but it could never suffer a catastrophic defeat, either.) The navy was the hand that gripped Europe by the throat, not to be disgorged unless it suited the British to do so. If you can manage it, ask the shade of Napoleon which he would rather have removed: the British redcoats, or the British navy. The latter, beyond all doubt. Why did the Kaiser enter into the arms race that figured so heavily in igniting WWI? Certainly not because he feared the "Old Contemptibles." Why did Germany lose that same war? Primarily because its seas were controlled by the British navy, and not vice versa.
Finally, it is worth noting that the British army that won India was primarily a *native* army led by a few Brits--*not* an army of redcoats by any stretch of the imagination.
Of course, this all don't have much to do with UU's, except as historically apt or no. For the US, you could make a case for 18th century Rangers/Kentucky riflemen, carrier groups, or air assault divisions; nothing else is really that unique to the US--well, maybe the B17. Or possibly artillery; US fire control systems are & have been since WWII the best in the world. Nothing spoils a baddie's breakfast like a perfect TOT salvo from every tube in the division