It's an isolationist policy. The US military doesn't have military bases/presences across Europe (and elsewhere) out of the goodness of its heart or to protect Europe. They also do it because their military realises that its much, much better to have bases somewhere where they can strike an international enemy quickly from. It's a militarily mutually beneficial arrangement.

So, the US would lose that early strike capability. They'd also lose all the intelligence benefits having people on the ground brings with it. Also, should it happen and Europe was successfully invaded, US businesses would either temporarily or permanently lose access to one of their biggest trade export blocs and a large amount of access to imports too.