We tend to stay in timeshare units, so we normally have a washer and dryer in our room. I have used the machines at BWV, ASMu, and SSR. It's obviously more convenient when it's in my room, but it was never a big deal to me to go do it. I've put it in and left it and I've also babysat it and just brought something to do. I like doing laundry on vacation. It allows me to pack less, I can promptly tend to any stains, and I don't have to go back home with loads of laundry that need to be done.
I would opt to save the money and have less luggage to wrangle. My one caveat is don't spend as much on replacement items as you would on the fee (i.e. any toilitries you have to buy down there, the detergent itself, etc).
As others have mentioned, utilize the personal item for packing too. Spilt toiletries between carry-ons if needed. Also, wear items that would take up a lot of space. Like don't wear your flip flops on the plane wear your sneakers. It's more annoying at security, but it saves a lot of room in your luggage (I wouldn't recommend this for small children or those with mobility issues, but everyone else will be fine taking an extra minute or less putting their sneakers back on). This would also apply to things like wide brim hats, hoodies, and jeans (as opposed to going in a sundress or shorts). Weather obviously plays into this as well, you don't want to be wearing jeans when you're landing in a 95 degree Orlando.