The President is the Commander-in-Chief, and Americans usually have a marginally higher amount of trust in their civilian President than the military authority in the JCS. (Usually.) For whatever reason, it doesn't reflect well on a President to leave grand strategy to the generals. Most Americans would prefer their President to, even if he (or she) has relatively little military experience, at least enough knowledge to make a military decision that doesn't rely solely on what the military tells said President.Why is military leadership so important? Don't you have generals etc?
Its not even a blip on the radar in the UK politics..
Besides, compare the UK military effort right now to the US one.

EDIT: I am a slow crossposter.