I disagree. There was a lot of debate during the Cold War that if the USSR had openly stated that they would invade Europe but would not attack the USA, whether the USA would risk annihilation to defend Europe.
If it came to the crunch would America really risk certain death of themselves and their families for the French and British?
In cases like that you have to have a deterrent of your own just in case.
The Cold War is over. Russia doesn't have the capacity to successfully invade Sweden, never mind the rest of Europe.
Who would invade us if Britain lost it's nukes?