4:27
“The time when we conveniently let the United States carry the burden for our security is over. The US is absolutely committed to NATO, but this commitment comes with a clear and long standing expectation, that Europe and Canada take more responsibly for their own security, and I believe that is only fair.” -Mark Rutte
It seems to me that the objectives until ~2014 were to (a) provide moral and a small amount of physical support for the War on Terror; (b) sell US weapons, such as the F-35; and (c) ensure that European defence centered around NATO, under US control, and not the EU. The US wanted Europe to have enough capability to assist the US, but not to go off on adventures of its own and certainly not (going all the way back to the Washington Naval Treaty here) enough military might to resist the US or start another European empire.
That is, the strategy from WW2 until fairly recently was to prevent Germany re-arming. Just as the large deployment in Japan is to prevent Japan from re-arming just as much as it is there to defend the Pacific from China.
I wouldn't call 35000 troops of mostly non-combat specializations a "huge number". In the Cold War, the American presence in West Germany was an order of magnitude larger, about quarter a million soldiers.
"Defence, or occupation?"
Neither/nor. Logistics for various distant operations. Rhineland is a very practical stop located between the US and the Middle East + North Africa (MENA), closer to MENA, with highly developed maintenance and repair facilities, communication facilities, top-notch hospitals for casualties etc.
If a GI Joe gets seriously injured in Kabul or Baghdad or now possibly Tehran, they are airlifted to Ramstein. If an armored vehicle gets damaged by a roadside bomb and the local mechanics cannot fix it on the spot, dtto.
General Hodges wrote several articles on how dumb the current administration is to alienate Europe, because without access to such facilities, any deployment in the wider region becomes very challenging. Even the original invasion of Iraq was somewhat complicated by the Irish refusing the use of Shannon airport for US military aircraft.
https://unherd.com/2017/10/keeping-russians-americans-german...