This 100x. If you go down the route of a generalist (and not just "generalist engineer" but generalist in marketing, engineering, back office, etc.), then you will quickly find yourself unemployable in the traditional sense since you will no longer ft any job description.
Maybe you can still wing it if you have a strong network, but if you plan on being employed rather than running a business, err on the side of being a specialist but keep your eye open for shifts in trends and don't become complacent on your existing skill set.
Yup- we'll see what's in store for me if I ever have to go through the bigco PM interview gauntlet again! Not even sure I'll pass the resume screen even if I'm friends with the hiring manager! ;)
To be employed, you'll do better as a specialist. If you pick the right specialization.