Where are system administrators in the real world?
I think that one of the most challenging things about attempting to understand what a system administrator is comes from the fact that the title of system administrator is often given out, willy nilly, by companies with little to no understanding of Information Technology (IT), systems, or administration and treat it like a general filler for IT roles that they do not understand or know how to name. It also has a strong tendency to be given out in lieu of pay raises or promotions to entice junior staff to remain in an otherwise unrewarding job in the hopes that an impressive title will help them later in their career, so much so that in the end, the number of people working as system administrators is a very small number of people compared to the number of people with the title. In fact, it is no small stretch to guess that the average person with the title of system administrator has never thought about the meaning of the title and may have little inkling of what someone in that role would be expected to do.
If we look solely by title, system administrators are everywhere. But they exist mostly at companies too small to have plausibly employed a system administrator at all. Systems administration as a dedicated job is nearly exclusive to large companies. Most companies need someone to do the tasks of system administration, but only as a part of, and often only a small part of, their overall duties. It is the nature of IT that in small and medium sized companies you typically have generalists who wear many hats and do every needed IT role while having little to no time to focus on any one specific function. Whereas in large enterprises you generally get focused roles, often grouped into focused departments, that do just a single IT role: such as system administrator. But even in some enterprises you find departments organized like separate, small businesses and still having generalists doing many different tasks rather than separating out duties to lots of different people.
There is nothing wrong with this, of course. It is totally expected. It's much like how, as a homeowner, you will often do a lot of work on the house yourself, or you might hire a handyman who can do pretty much whatever is needed. You might need some plumbing, painting, carpentry, wiring, or whatever done. Whether you do it yourself, or your handyman does, you do not refer to either of yourselves as plumbers, painters, carpenters, and others. You are just a handy person, or the person that you hired is. You still recognize that a dedicated, full time, focused plumber, painter, carpenter, or electrician is a specialized role. You might do all those tasks occasionally, you might even be good at it, but it's not the same as if that was your full-time career. If you decided to claim to be these things to your friends, they would quickly call you out on the fact that you are quite obviously not those things.
System administrators are like plumbers. Everyone who owns a house does at least a little plumbing. A handyman who does home maintenance full time might do a fair amount of plumbing. But neither is a plumber. A very large housing development, or a construction crew might have a dedicated plumber on staff. Maybe even more than one. And nearly every homeowner must engage one from time to time. If you are me, regularly. Most plumbers either work for large companies that have need of continuous plumbing services or they work for plumbing contracting firms and have the benefits of peers and mentors to help them advance in their knowledge.
Nearly every business no matter what size we are talking about needs system administration tasks done. For very small businesses it is not uncommon for these tasks to amount to no more than a few hours per year, and when needed the scheduling is often unpredictable with many hours needed all at once and large gaps of time in which nothing is needed. In large businesses, you might need tens of thousands of hours of system administration tasks per week and require entire departments of dedicated specialists. So just like plumbers, you find small businesses either hiring IT generalists (akin to the homeowner's handyman) or outsourcing system administration tasks to an outside firm like an Managed Service Provider (commonly referred to as an MSP) or keeping a consultant on retainer; and you will find large companies typically hiring full time specialist system administrators that do nothing else and work only for that firm.
System administration tasks exist in every business, in every industry and create the foundation of what I feel is one of the most rewarding roles within the IT field. With system administration skills you can chart your own course to work in a large firm, be a consultant, join a service provider, or enhance other skills to make yourself a better and more advanced specialist. Without a firm foundation in system administration a generalist will lack one of the most core skills and have little ability to advance even in the generalist ranks. And at the top of the generalist field, true CIO roles primarily pull from those with extensive system administration comprehension.
At this point we know what a system administrator is, where you will find them in businesses, and why you might want to pursue system administration either as your career focus or as an enhancement to a career as a generalist. Now we can go into real detail about what a system administrator really does!