This really depends on your employer and your definition of specialist. There are jobs where following a very straight career path would be a disadvantage: you might be perceived as a boring candidate who would potentially struggle if given work outside their domain. I think it's fair to say that, generally, breadth is valued more at smaller companies where people have to multi-task.
In academia it's much easier to do well as an inter-disciplinary researcher than it is to try and be the best in a single field. The obvious killer combo right now is machine learning for X, where X is a field which does not have a strong grounding in computer science. Hacker news gives a very skewed view on the world, as if everyone is up to date with the latest developments in deep learning. In reality, most people in academia are pretty unaware of what's possible, or don't have the technical skills (or grad students with them) to make use of it. This is currently true even for maths-heavy fields like physics, which you may find surprising - I certainly do. Now is a really good time to get on the ladder.
You also need to consider job satisfaction. People who are pretty good at several things may be bored with a single track career, and no amount of money will make up for that.