What you can "do-it-yourself" has come a long way from just home improvement. Now there are things like teeth whitening and hair waxing that you can do-it-yourself.
Whitening your own teeth does not make you a dentist, though. Dentists make their money from the people who either don't know how to take care of their teeth, or are really bad at it. Sometimes a dude with perfect teeth gets some of them knocked out, through no fault of his own, and the dentist is there to fix it. Even if you never need more dental work than cleaning and polishing, you at least need to have that trained professional to look in your mouth and see that your teeth are, in fact, just fine.
The division of labor is something necessary for a civilization to advance. A few people focusing on doing one thing really well is better than everyone trying to do everything half-assedly. Sure, it would be nice to learn how to do my own electrical wiring and plumbing... but fuck that noise. I am going to call up a dude in the phone book and pay him some money to do it for me.
That being said, of course, there is a value in learning how to do some kind of craft yourself. This is because we live in a "knowledge economy" where what you learn in college is just specialized information to... do things with information. And people. Maybe also computers. It's rather fleeting, and sometimes unfulfilling. There's very little you can look at and say, "I did that. I made that. I fixed that." This is the point being made in Matthew Crawford's book Shop Class as Soul Craft. I have not yet read it, but it's on my growing list of "books I should read eventually." Part of the book was adapted into an essay for the New York Times, title The Case For Working With Your Hands. I'd say that you should go read it, because you can do so for free. And if you like that essay, you should read his whole book. Probably. Like I said, I haven't read it.
I suppose the point I am making here is the opposite of what it originally sounded like I was going to make. You cannot be your own dentist, and there is a value in paying a professional to do things for you, but there is also a value in being able to do things with your hands, be it fixing things, crafting, or whatever. That value is not just a practical one, but one that extends into your feelings of worth as a person. You are faced with tangible problems, and you yield tangible results. It is so much more than just knowing a bunch of things, and the worth in that is something that can't go in an Excel spreadsheet.