Having bases in Europe allows the US to punch beyond its weight. Aircraft Carriers can’t do it all.
The US can project power well beyond our borders because we have military bases well beyond our borders.
Bringing the troops home would eventually save money but we would loose all of that money and more when we had to reestablish those military assets. Keeping the peace is much cheaper than reestablishing the peace.
What these bases have bought us is keeping large conflicts from developing from small conflicts. From these forward bases we can quickly project military power to hot spots in the region. These bases also have large well equipped hospitals for treating casualties and provide our troops the best care available in the region.
At first glance it may seem like we are providing Europe free defense but think a second time and you may see that we are preventing our entry in to the Third World War which would be much more costly.
I disagree. If we were to leave Germany today, Germany would be forced to pony up and fill their own void. Us being there does nothing but allow them to fund their own socialism without running huge deficits and allow them to project power and financially blackmail our allies in the EU. Unless there is an imminent threat or we are gaining wealth or resources, I oppose projecting power well beyond our borders.