Yes I am sure specialisation helps, but as you have rightly pointed out the amount of stuff you need to know even with one language/one platform is enormous.
It's insane. At one point I was fully fluent in C#, Silverlight, all the HTML/CSS/Javascript necessary to successfully embed Silverlight, MVC/MVVM, SQL implementation and design, etc etc etc etc... Being a full stack .NET programmer is just as crazy as being a full stack Javascript.