A long time ago, at least, a long time in the eyes of my kids, I worked for a large organization as a production DBA. We had a generic monitoring tool, but it wasn't SQL Server specific. I ended up writing my own enhancements for the tool that used its data, as well as gathering other SQL Server specific items into a local database on each instance. From there, I had this data copied to a central location each night and a report generated. This helped us with ISO certification (originally) and later, Sarbanes-Oxley compliance.
I was reminded of that when I read Pamela Mooney's post on Things You Should Know About Your Server. She follows the simple method of ensuring each server monitors itself and rolls up that data. This works well, even if I'd never want to do this again. The time I spent building a monitoring system wasn't really time well spent. These days I'd buy some monitoring software and then query that data, bother the vendor for enhancements and have either a notebook or a smaller set of processes that gathered specific data I might need. Likely I'd use XE and some stored query data, but if I monitor infrastructure, I don't want to have to worry about building and maintaining monitoring software.
The main point from Pamela's post, however, is that she seeks awareness of how the systems work. That's the key for a successful sysadmin of any system. You should not, and do not want to, check each system every day, but you do want to know how to find out what is "normal" quickly and be aware of changes. We want to quickly narrow down potential and possible problems because of our experience and history with some server/instance/application/etc.
Most of us get calls on a few systems regularly. We may know those well, but often we're fire fighting and normal can be an elusive definition. There are often many systems that we rarely get called to examine, but most good DBAs I know have some idea of how almost every system performs. Having a little data available quickly allows us to diagnose whether a problem is real or imaginary, chronic or transient, as well as how to proceed to resolve any issue.
Awareness is an important skill when dealing with anything on a regular basis in your life. Certainly in parts of life outside of work, but even at work, paying attention and having some idea how how your environment should work will help you catch, diagnose, and solve issues. The best DBAs might do this before the client even calls.