Not trying to argue with you, I just happen to have a counter-point on everything you mentioned LOL.
> wasting time going down an unproductive path
This is usually a fallacy. First, in most cases, what's the hurry? You're learning things along the journey. A self-taught programmer will encounter this problem once, then know about qsort for the future. No 4 year degree required. Second, if the bubble sort gave them the performance they needed, they wouldn't care to find the qsort solution. If the performance was a problem, it's likely they would stumble upon qsort as a potential solution. Third, we see professionals with fancy degrees and well funded companies build by smart people leak plaintext passwords all the time. Don't roll your own crypto is wise advice but I think anyone that searches "how to make a login system" or "how to store passwords" is going to find that advice. All to say, the 4 year degree doesn't necessarily protect you from making this mistake.
> Yes, I look at yootoob instructional videos. Watching it in person is far more instructive.
I have the same passion for making. I build homes as a hobby. Learned it from youtube. I find if I struggle with a tool, it's because I just haven't used it enough. However, I approach the same situation you mention a bit differently around professionals. Maybe due to my self-taught nature but, I do research on the problem ahead of time. I basically know exactly how to fix the problem but don't want to - or just lack confidence in my ability to execute it (drywall finishing is easy, in theory, I suck at it so I hire it out every time). Usually I look at the multiple ways the problem is usually solved and form my own opinion about how I want it done in my case. If you dig enough, you'll find the pros and cons of most solutions. There's usually videos comparing the methodologies on YT. I study all that as if I'm going to fix it myself from soup to nuts. So basically, I'm ask how the pro plans on doing his work, what products he's using, how long between steps (if something has to cure), what tools and material he plans on using, etc. Then, I will challenge his way if I think he's missing a step or taking a shortcut. I will also watch during his execution and tell him if something doesn't look right so he can fix it before it gets too far ahead. Of course, I ask questions and do so more friendly so as not to be a judgmental prick constantly critiquing them. But, I've already done so much research and seen the tools in use that I'm rarely surprised by how something is being used or it's existence.
Probably one exception is fine carpentry and furniture making. I never had interest in those things and there is a whole world of specialty tools that I've never stumbled upon. I also don't really have much need for that specialty as I just buy furniture and don't have a historical home myself, the modern architecture homes I build doesn't have much need for it beyond custom closet systems and cabinetry (which is built off site)
> BTW, the number of people who seem to be capable of self-teaching themselves calculus seems to be very small
Well, I'd argue that the number of people interested in doing this is already very small and the key is to be resourceful in your instruction. You can ask for help when self learning. But that doesn't mean you have to signup for a semester long course that covers one topic a week. Jump on Udemy or similar and I'm sure most people with the right drive, will learn it. "Self-teaching themselves" doesn't have to mean doing it yourself or re-inventing the wheel. However, when you don't need to learn something as part of a larger goal (like a pre-req for your 4 year degree) then it's easy to give up when it's a hard subject. People rarely need to know calculus unless they're in school.