It seems to be a case of the person selling the shovels making more than all the gold miners combined?

why do carmakers not sell cars directly?

Not even close.

Car makers actually manufacture something of value: cars. They manufacture those cars to maximize profit because that's the best way for them to make money. Car makers are not selling a way for others to make cars. Get it?

If you are an amazing player, coaching others would not be the most profitable path. If your skills are so good that others need to become like you, you would keep those skills to yourself and not teach the competition how to beat you.

I coached for a few reasons for a very long time.

1. Variance Free Income
2. I enjoyed being an expert on something and people taking my opinions seriously
3. There are so many things to remember about the game that explaining them to others helped keep me sharp when I wanted to play. I would practice what I preach.
4. I love to learn, and love to teach, and I hate to grind. Its very taxing and boring only to grind in silience every day in front of a computer screen.
5. Im a people person, and so I enjoy talking about poker with new friends I make as students, instead of constantly grinding out profits.
6. You can make alot of money coaching, and its variance free money which is a huge benefit to the coach.

If i recall most coaches do play but ik few dont

I coach for profits.
I coach because i keeps me from spazzing and doing dumb stuff wen I play.
Sometimes when I'm viewing a hand that hasn't been played by me I have a better time seeing other merits and reviewing HH's that aren't mine.
I like to sweat someone else.

I enjoy it.

Coaching often made me a better player when I did it. You're forced to explain and defend potentially everything you say or do. If you get into that habit, it really keeps you on the ball as far as staying on top of improving your own decision making and seeking more solid answers in many situations.

I used to track coaches that made videos full time in the games I played, and almost every single one of them improved their results quite drastically after making videos. That isn't 100% from making those videos, since the ones that tended to stay around a long time consistently obviously had better work ethic and dedication to the game than others.

More generally, there's a large market for coaching and an overreaction to results (graphs), so having some solid results means that coaches can often instantly command a very high price for coaching, whether they are experienced/any good at teaching others or not. And a coach with good results who also has a reputation as a very good coach can be worth a great deal of money in the marketplace. So supply-demand is a big factor here too.

And finally, even though many students probably don't get full value (often because they don't give the game enough of a serious and long look... IE they don't put in the focused, tilt free hours required to succeed), the ones that do will point to coaching as a fantastic deal in many cases. So the potential for the coaching to help you improve to a very high degree also drives many students towards it.

Thanks for the good answer.

when one teaches two learn