Laundry not working ETA: Solved - Sim must change in a room.
For some reason, my game chose to not trigger the laundry system despite having all the possible equipment it would require for the system to function (hamper, washer and dryer). As you can see in the screenshot, my lot has the university (which I only content that brings said feature) laundry related objects. Though the last time I remember it working perfectly is when I played in a Sims University dorm. If you need to know what I'm using, I will gladly list them.