So the healthcare, food, housing, etc. they do come out of a soldiers paychecks. There is a reason why the soldiers pay has become a more talked about thing because their pay is lower in part to pay for these benefits. Social supports are also available to literally all Americans so that isnt something that is military specific.

Its not correct though that they get free relocation assistance. They get X amount of pounds that they can move. Also soldiers can be "fired" its a dishonorable discharge or a "less than honorable discharge."

Planned economies might be a way to describe the foreign bases but that isnt how it is in the American ones.

Parts might sounds socialized but I dont see it that way strictly because this is something they opted into, something they are taking less pay to be part of, they cant easily get out of their contract, and they could be sent off to die at a drop of the hat. Willing to die kinda gets you extra benefits.

All of this can really be compared to how when you get job offers in the US and the company offers you XYZ benefits. Microsoft and Apple and two huge people who are known to have laundry services and all sorts of crazy perks for working with them. The US army is the same.