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 later. I wouldn't complain if they hadn't advertised this, but they literally said in one of their blog posts that we could run a laundromat. We need them to include "wait for laundry" and "dry laundry" in the business activities tab, or something.
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.
It's kind of silly some of the things they included in the pack that they had to have known wouldn't work. I've only ever seen sims with the neat trait autonomously press the button to wash or dry clothes, and even with the trait they barely ever do it. I've never seen a sim without the neat trait autonomously even try to do laundry.
There's just no way a laundry mat would work on its own. You'd need to offer another activity for sims to stick around and then have a sim that you controlled constantly doing laundry to keep the machines clear.
Edit: Noticed that I spelled laundromat "Laundry mat." I didn't change it because that's funny.
Nothing to say about solving this one, but I will say it's not necessarily "a bug", but an aspect of how activities work. essentially, Business Activities simply push a list of interactions on Sims- they don't give them a chain of commands that flow into each other. They quite literally tell the Sims "Do these interactions while you're here". Several things had new autonomous versions added for this exact reason, as they weren't doable by non-played Sims before at all.
For Laundry, the tuning looks like this:
The activity literally tells sims they are allowed to put things in washers, take things out of washers, put things in dryers, and take things out of dryers. Since you can't do the last 3 until the first is done, and has time to complete, the result is that sims show up, do the only available option of putting laundry into a washer, and then have nothing to do, and leave.
If your business has other things to do, they may stick aroudn long enough to do the other actions...but there's nothing guiding them to do their laundry, so you'll see customers take laundry from a machine they didn't even use and move it to a dryer.
This is less a bug and more a major design oversight, and it won't be "fixed"...it'll be implemented, as it's currently just simply not implemented at all. I'm not sure how this one made it to release, as it would take literally the most basic testing to realize that this isn't going to work at all.
My suggestion would be that when a Sim does the first interaction they are given a buff that encourages them to stick around a set amount of time, and when the buff disappears, pushes the interaction to move clothes to a dryer. This still wouldn't solve the issue of Sims using random washers/dryers, though, and they'd all be competing for whatever was available at all times. Essentially this needs to be its own entire new system to actually work right, so don't hold your breath, considering we're still playing the game where Thriftea basically doesn't work whatsoever.
Adding weight to the post, have just created a sim that has made a laundromat (small business residential). Some customer sims will put loads in the washing machine, occasionally they will subsequently start the wash, but then they do nothing. Many sims will go to put washing into the machine, but will bug out and it will dump a pile on the floor (it might be that one of the things for customers to do is read books, I notice they also dump a book on the floor beside the dumped laundry pile.
My workaround for gameplay is to set up some sales shelves, have my sim complete the wash/dry cycles (including washing the laundry on dumped on the ground), and then set it on the sales shelves - my head canon is that sims who are purchasing it are paying for her to wash their laundry and returning next day to collect it, ie paying on collection).
But of course, that is not true to how a laundromat works.
I believe it should be noted that when Sims visits your business lot, they don't complete their tasks from start to finish. For example, when setting up a laundromat, they will start washing their clothes but then leave the lot, leaving players frustrated. It would be great if Sims could complete the entire laundry cycle on there own instead. It would enhance the gameplay experience if we didn't have to manually transfer each load to the dryer ourselves.