You actually never improve the laundromat! It’s like having a front. You expand for the arcade and eventually begin to encroach in the laundromat space even. Don’t want to spoil more, there’s a little story there.
I get the skepticism but the game is not literally running a laundromat - it’s an early source of income primarily that you juggle as you make the arcade work. It’s a series of little mini games/timing events to generate income and eventually not do laundry anymore. That being said, if you are patient and kind of dive right in, you could technically never do anything in the laundromat ever and still do the game.