Why US troops could remain in a British-defended Europe

Would the United States still station troops in Europe if a stronger Britain could defend it?

Yes; the deployment would help bind Anglo-American strategy and foreign policy together, beyond the number of troops strictly needed for defence.

Even if a stronger Britain could meet Europe's military needs, American troops would still have a political purpose there. Shared deployment would bind Anglo-American commitments against a third power. The same reasoning applies to the American desire for British and French forces in Germany. Joining military commitments helps bring the participating states' foreign policies together.