How could the security of the u. s. depend on the survival of an ally?

No America (the US) is unusual in history. It's continent wide size, natural resources, and great distance from other continents means it doesn't have to rely on anyone. US allies, NATO, UN, etc. are just political conveniences, to promote US trade and world stability and peace.
If all US allies disappeared tomorrow, no one in the US would notice.
This 'has' happened before in history when the US practiced 'isolationism' and shut itself off from the rest of the world.
America's allies only benefit the allies and to some extent US business, America doesn't need the allies, but America does need world peace and stabilityand that means allies.