I have the opposite experience. Being a generalist allowed me to "climb" fast at my current company as I am able to lead projects holistically and coordinate cross-functional teams.
I have no shortage of attractive offers, but more importantly I like to work this way. I can't imagine limiting myself to just one narrow area and ignore the big picture and so far it looks like I do not need to.
As for job descriptions: I would love to hire more of these people but it is difficult to put a job description through the system that would not be confusing. Thus, even I have written job descriptions for one specialisation that should be dominant, but in the fine print I make it clear that I am searching for someone with broader scope and will to basically "do what is needed".
PS: Thinking about it more... do you think industry legends like Jeff Dean or John Carmack fit more into the generalist archetype or are they narrow specialists?