Mechanic's school was a long time ago for me. I didn't do it for a living for very long, but I still do all my own work for everything: house, car, appliances, etc.
A few things my instructor told me still echo in my brain. He used to say "most mechanics are just parts changers." To reliably fix things, you have to intimately understand how they work. This is easier said than done when you fix a wide variety of things like I do. 20 years ago, if you didn't have the manual or the personal expertise, you had to find someone who did, or guess. Now, through the wonderment of the google-machine, most of the time whatever you want to know is a simple search away.
Obviously there's more guesswork in figuring out something new, like a gas RV oven recently for me. But taking the time to understand how what you are working on works, almost always pays off. Reading the manual, finding out what other people are saying, watching videos, etc., gives you an advantage before you take something apart, or replace a part you didn't need to replace.
Sometimes the time it would take to troubleshoot a part is proportional to the cost of the part. For those times, I have the attitude that if I have to take the part out to check it, I might as well just replace it. But when the parts are expensive and the labor is cheap, you really want to understand intimately why what your trying to fix isn't working.
Sometimes being able to troubleshoot and understand a problem isn't completely possible because you lack some tool or technology to diagnose the problem. Understanding how it works is still helpful, and will let you make a more educated guess.
This is why I am almost always willing to buy whatever specialized tools I need, within reason. For example, the $35 engine code reader has taken the mystery out of dozens of "check engine light" events for myself, friends and family.
Sometimes you want to know for 100% fact that something is perfect. You want to change the parts because you want all the best parts. This is about the only time it's beneficial being a parts changer. No need to check it or troubleshooting something you already intend to replace!