I'm not sure if "rent-seeking" is the right term to describe it, but an inevitable thing about your hypothetical plumber is that while he may be making more money, his new customers are getting a worse for the price (ads are expensive) plumber.
He will gain market power in his local market though, which could lead to his expansion and the closing of his least successful competition, bringing down area plumbing wages and allowing him to scoop up bad and inexperienced plumbers at a discount.
After that, we don't have to worry about his skills because he isn't working as a plumber anymore. He'll instead be paying bad plumbers bad wages, and keeping all the profits for himself. His desire will be to lower prices while expanding advertising, so the only variable to be played with is plumbers' wages vs. profit margins. He could then make high wage offers to the more skilled plumbers working for his competition in order to kill them off, and each time another independent shop dies, more of the wages will be shifted to profits.
Eventually, the market is served by the same set of plumbers as before (or likely fewer because some will leave the profession or the area), working at lower wages, but charging higher prices, whose excess goes directly to the shrewd marketer plumber. That's when our plumber enters local politics.
He will gain market power in his local market though, which could lead to his expansion and the closing of his least successful competition, bringing down area plumbing wages and allowing him to scoop up bad and inexperienced plumbers at a discount.
After that, we don't have to worry about his skills because he isn't working as a plumber anymore. He'll instead be paying bad plumbers bad wages, and keeping all the profits for himself. His desire will be to lower prices while expanding advertising, so the only variable to be played with is plumbers' wages vs. profit margins. He could then make high wage offers to the more skilled plumbers working for his competition in order to kill them off, and each time another independent shop dies, more of the wages will be shifted to profits.
Eventually, the market is served by the same set of plumbers as before (or likely fewer because some will leave the profession or the area), working at lower wages, but charging higher prices, whose excess goes directly to the shrewd marketer plumber. That's when our plumber enters local politics.
Maybe it is rent-seeking.