US/NATO have military all over Europe, and that hasn't prevented this either. The reason the threat doesn't work is because Ukraine isn't a NATO member.
The US has been pulling troops out of Europe for the last 20 years, and during that time, NATO's policy has been letting Putin walk all over its neighbors. If NATO stood up 8 years ago like they're doing today, then there would never have been a second invasion of Ukraine to begin with.