This is a tripwire to spike cost of taking by force. Europe doesn't have the blue-water navy or air power to fight a peer war with America but also does not need to.
Europe cannot fight a peer war with America: on day one the Americans cut off our cloud services, and all government administration falls over.
(logical consequence of this is that the US invading Greenland is really bad for any US startups, such as one might find on HN, because it makes the EU much more likely to respond with "local only" rules)
That's a two way street. Tens of thousands soldiers on European soil becoming PoWs. US Equipment in European bases like Air Force or Preposition Army Stocks impounded by Europeans. Logistics going further east via Ramstein - effectively whole Middle east cut off from US reach. Access to early warning radars in Europe also gone. Ability to rearm and refuel ships pushed all the way back to USA.
We switched their email off would be a political joke compared to tens of thousand soldiers stuck behind enemy lines. And that's all working with assumptions that EU won't nationalize European part of AWS/Azure/GC/(other US cloud providers) to force it to continue its operation.
Don't forget things like cutting off trade with the US, or trying to organize a dump of their debt to attack the currency. Or, trying for hack-attacks on key US network components. None of these involve "traditional military" but they'd affect the randos at home quite a bit.
