Aren't singletons the whole goal of Spring?
By contrast, using singletons in plain old Java, you'd have to go through and find every usage of SingletonClass.instance().everyMethodCallOnThisClass() and push it up to the constructor. Since you now have a new dependency you have to pass all the way down your callstack, it can get painful quickly.
You still have the issue of global state, but I think that's altogether more complicated. Sometimes state really is global to your program and exposing it everything makes a certain amount of sense. It may well be ok for managing system resources (thread pools, network connections, IO in general). I think often you can get away with a boolean flag or two shared across a whole app. If it's read-only it's not a problem at all.
You need to be aware that every bit of shared state you make available or continue to use is a potential source of bugs and maintenance. Every bit of this that you expose needs serious thought. Don't let it snowball. Even if it means you have to make a few extra types of object or pass a stupid number of arguments all the way down the callstack, that's usually preferable because at least then you can reason about what's going on.
I didn't know about the other scopes though