The only business activity available is to do laundry, but sims won't wait for them or try to dry them. They will literally put clothing in the washing machine and leave the business a few moments la...
Ideas
Fun fact: This was already so in Sims 3 laundromats. It seems impossible to code the whole washing process for NPCs. Perhaps turning off free will may help?
Butlers and maids in Sims 4 will come back later to move the laundry, start the drier, and take the dry clothes out. I've had them entirely handle my household laundry for years when I have a butler/maid, though I do have to select "put away" on the folded stacks they leave near the drier. The thing is they do not stand there for the entire process, they simply start it, go to their next task (dishes etc), and see there's an action ready later to come back.
So I don't think it's unrealistic to get NPCs completing laundry in a laundromat. However I think the NPCs should not be picky about which set of laundry is theirs, and should simply move and dry any available laundry. Loads getting moved through is much more important than one sim following "their" load all the way through the process, so that laundry is happening, instead of the player needing to constantly clear out a mountain of abandoned laundry.