As a generalist, I agree with bulk of what you're saying but at least my personal experience seems to echo the fact that generalists in general are undervalued since when someone asks a person "what can you do for me", a specialist always has a better and sharper answer than a generalist - and that makes all the difference.
Personally I'll take a generalist any day since specialists suffer from the "if you only have a hammer everything looks like a nail" syndrome.
Having said that, my 1 career advice to anyone would be, become a specialist in 1-single thing, and then become a generalist in everything else. I'm not that, but I feel that that I would have been best served if I had been that.