Absolutely, making more money is a big motivator for entrepreneurs across the board, including plumbing entrepreneurs.
I found the documentary "Jiro dreams of sushi" illustrative (in the opposite extreme). I believe most of us would fall somewhere in between (... aaaand, we get to Maslow again :)
If by "change the world" you mean narcissistic grandiosity about being in the history books, yeah, that's generally ridiculous. But small things also change the world. Raising kids. Installing sinks. Fixing roofs. Serving a meal. All of these things make the world a little better.
This is distinct from what Graeber called "bullshit jobs". Making sure that you use the new cover sheet on the TPS report that nobody will read, for example. Some people are happy doing bullshit. But trades have the appeal of doing something undeniably real, undeniably beneficial.
So yes, as I said, I believe that somebody who started a solo plumbing business is absolutely thinking of making the world a better place. And I think they do it every day.
For the tradespeople I have known, the answer is yes. They also like getting paid, of course. But they find satisfaction in making the world better one sink at a time. Otherwise spending 40 years as plumber would be an absolutely miserable experience.