I wish they wouldn’t break up the union (for the reasons you mention... I do think they are valid). But I also value the right of people to separate from political entities they no longer wish to be part of.
As far as anti-Americanism goes, It’s been 6 years since I was in Scotland. Unless things have changes, anti-Americanism is limited. The worst I heard were bad jokes about us. Had a great time there on all my trips and never once felt unwelcome (except the time I got bit on the shoulder but I think that might have been a show of affection).
Granted, how people treat individuals is different than how nations deal with other nations. But I still believe that the Scots have enough ties to the USA that we’d get along just fine.
Personally, I hope for Devo-Max, the Scots get control over everything except foreign and defence policy. The UK has many burdens that require it to have a strong military, particularly a navy, and it is of course well known that Scots provide some of the best in the British army.
If the Falklands were to happen again, would the UK have to fight alone, minus the Scots? The Irish already have a policy of strict neutrality, which basically means they freeload off the security provided by their neighbours. The UK will be struggling to shoulder the burdens protecting this country and the civilised world from what it is plain to see is an increasingly dangerous world. Scotland, for its part, will lose the powerful and influential soft power excercised by the Foreign office, which according to reports I have seen, is second only to the US in influence on the world stage. Independence would be a tragedy for Scotland, and would make life more difficult for us. We would see a diminished UK, and a Scotland that counted for nothing.