There's rarely anything old school sysadmins have learned that hasn't come from experience.
Been there, done that, fought that shit the first time. And the second. And the third. (it's amazing how often I find myself solving what are essentially the same problems over and over.) It's one reason why you'll find we'll push back on the "ohh shiny". There are many wonderful and fascinating things coming out. Tech is an amazing field to be working in. But it's also ridiculously frustrating because no one pays any attention to _why_ things are done the way they are, or _why_ approaches haven't worked in the past (I'm all for re-introducing past failed approaches, as long as there's evidence those reasons have been investigated)
You'll find a common trend amongst us in that most of us sort of ended up in the role accidentally. Schools and college teach you to become developers. Few people tend to head to college with the view of specialising in the ops side of things.
Even speaking as a comparatively old-school sysadmin, my strengths come from being flexible and adaptable. What I do today is nothing like what I was doing 5 years ago, and what I did then is nothing like what I was doing 5 years before that, and so on down the line. The field is constantly in flux.
I just have the best part of two decades of experience to both anticipate the problems, and be able to get to diagnosis quicker when things do go wrong.
Even as the older sysadmins die off I'm fairly confident there will be newer ones to replace them, because people are going to continue to learn from the problems they run in to.