I am glad that Devops is bringing generalists out of the closet and showing how valuable they are and how much companies need them. Also, I would bet money that the majority of successful "specialists" have a fairly broad set of knowledge outside of their specific job function. So, your best generalist is a competent specialist, and your best specialist is a competent generalist.
So, "What makes a good generalist?"
Since we can only learn one thing at a time, I think most generalists started out as specialists (Solaris System Administrator, got CCNA certified, passed the MCSE test, Oracle certified, etc...). But, over time they gained knowledge outside of their special area in order to solve a problem. Over time that accumulation of knowledge became patterns of understanding they can use to synthesize information and make decisions. Finally they gain wisdom to have insight into things and project into the future.
I think one of the greatest contributions Devops makes is in shining a strong light on the fact that there is only one problem: The Business Problem. There is not a system problem and a software problem and a network problem and a security problem, there is only the business problem. The more everyone in the business knows about the rest of the business, the more they can understand how the parts relate, and ultimately make wise decisions to help the business succeed.
You can develop knowledge, understanding, and wisdom from others. One way to foster generalist growth is to rotate new employees through various departments when they are hired in order to give them a full picture of their peers. It's not quite cross-training because you don't need them to be competent in the job. It's more like cross-exposure so they can feel some of the pain and absorb some of the knowledge, understanding, and wisdom of the other departments. Every department has wisdom worth knowing. The level 1 CS person knows a lot about the software after the 10th customer calls up about a feature that doesn't work like it should. Or, the Ops person gains knowledge as they sift through all the "normal" errors in the log file to find the one, little "important" error buried in the noise. And the developer knows how to work with a team sharing a software repository; and knows what is the right version of the application and how a lifecycle is important for any code.
Our company rotates new developers into a support role which is a good start. I think it would be better if every Dev or Ops employee spent a week in some rotation like: Customer Support -> QA -> Security -> Development -> Operations to see the full context of their work and how it affects all departments and how all departments affect what they do.
When we have a broad knowledge of our business and feel some of the pain of our peers, I think we will be more successful at whatever specific role we have.