It turns out that applies to NATO, too. And would the current government actually want to be in NATO? So I guess Scots independence isn't really in the US interest.
There's a lot of romantic interest attached to the idea of history being made, but a lot of history has been made in our lifetime, and when it actually happens a lot of the time we don't actually notice.
The only direct interest the US has in Scotland is the submarine based Trident nuclear weapons that are home based in Scotland. England has no current capability to hold them.
Scotland wants to evict all nuclear weapons.
The US UK have a workaround that we would rent them space at one of our bases for 10 years while they construct one in England.
This is a short term issue.
Five million Leftist out of the UK electorate would result in a more pro-US Westminster government and higher GDP per capita UK.
If Quebec exited Canada then the remaining Anlo-Canada would be a much better US ally too.