As an American, this is a good thing. I don't want a world where Europe / UK are vassals to the hegemon. A European happy to live under America's boot rather than own their own destiny is a weak person indeed.
I can't imagine the EU should feel particularly different? (other than Ukraine and the recent shemozzle)
I don't think relying on your allies makes you a vassal.
As an American I encourage every country to decouple, and as I understand every country is working on it. Mark Carney of Canada said it best, it will never be the same, ever no matter what the future is because trust that has lasted 90 years has been broken. Canada will never have the same relationship with the USA.