But you can only see that in the movie version!
I haven’t seen the stage version, but the movie had a long scene between Marion and Harold, after she meets the anvil salesman, in which they discuss rumors and how hurtful they can be. She ultimately decides to trust Hill, the guy who got her brother to come out of his shell, instead of the vindictive anvil salesman, because Hill has been giving her the benefit of the doubt about Winthrop’s parternity, in spite of the gossip he’s heard from Mrs. Schinn and her committee. That scene wouldn’t work if Winthrop really was her son.
And furthermore, the impression is that Marion’s father and old Madison had remained friends right up until whichever of them died first. Which probably would not have been the case if Madison was Winthrop’s father.
As has been mentioned, there was no seriously shady, semi- or fully illegal get-rich scheme. Hill may not even have been shaving money off the top during the insrtument and uniform ordering. He may simply have been getting a fat commission from the grateful companies that sold these things, which would have been difficult sell in the practical midwest, regardless of their intrinsic quality.
The first musical number (the salesmend on the train) sets up the notion that there’s this amazing salesman out there who can actually get these simple farming communities to shell out big bucks for boy’s bands, through sheer sales persuasiveness. The implication (“But he doens’t know the territory!” “Doesn’t know the territory?” “What’s the fella’s line?” “Never worries 'bout his line!”) is that Hill is such a slick salesman, it really doesn’t matter what the product he’s being asked to sell is, or the the real needs of the people he’s being asked to sell it to. It’s suggested during the first River City scene that he used to be involved in some sort of scams (“I thought you was in steam automobiles?” “I was.” “What happened?” “Someone actually invented one!”), but really, the notion of him being a travelling salesman at all is supposed to make him shady from the start as it is.
The first River City musical number, where they sing “But what the heck? You’re welcome! Join us at the picnic! You can have your fill of all the food you bring yourself!” is meant to convey the notion that these are not people to be easily separated from their wallets. The “You Got Trouble” number shows him using his newfound knowledge of a pool hall in town plus the moral outrage of the town to mesmerize them into buying what he’s there to sell. Sure there was the Sears catalog, but how many tubas and french horns could those manufacturers actually sell to these people without someone like Hill on hand?
The whole thing was masterfully spoofed in the Simpsons’ monorail episode.
I think he waits around in town for uniforms to arrive in order to continue to cast his spell. If he took off, they might come to their senses before al the transactions had been completed. It could be that it’s COD. The thought that the esteemed Professor Harold Hill is going to personally oversee the instruction of the band that will save their town from moral degradation is what keeps them moderately complacent until it’s too late.
There is a line toward the end of the stage version where Hill tells (asks?) Tommy Djilas to go around and collect the money.