EMD360,
I'll give you my thoughts, though they may or may not help you much. We always have our towed with us, so we could make trips to a laundromat if need be. And we have a 36' Class A, not a "small" motorhome by most standards. But we did usually travel with the full family.
When we ordered our rig back in 2004, with 4 young kids, we knew we'd be needing storage space and didn't want to give up the utility closet to a washer/dryer unit. However, for a very modest additional charge, we WERE able to get a "washer/dryer prep" package which put the hot & cold water controls, drain and AC power in the utility closet should we wish to upgrade at a future date. That upgrade, I believe, also increased the water heater size from 6 gallons to 10 gallons, which was a good idea for a family of 6 any way.
Here we are 17 years later and still have the same rig, and hope to keep it rolling for quite some time. In all of those years, for our extended trips, we usually used coin operated machines at the campground. And that worked fine. We'd just schedule a "down day" during our stay to do the laundry.
But over the years, we also realized that MANY more times than needing our clothes washed, we needed our clothes or towels dried. That is, we came back from the beach, we got caught in a downpour, etc. and we had wet clothes and/or towels which needed to be dried. You can imagine with 5 and 6 of us in the rig, we could generate quite a pile of wet clothes if we got caught in a good drenching. You can't just hang them up in the shower, or bedroom or other part of the motorhome because we pretty much had 5 or 6 people plus a dog or two, so the rig didn't have much space to just hang clothes to dry. Hanging them outdoors isn't an option if it's raining or at night.
In those situations, a clothes dryer would have been really handy. Every time that happened, we were at a campground which had 50A service, so a small, electric 240V dryer would've done the trick for us nicely. Heck, even a 120V dryer would've been better than nothing. At least we could dry our clothes and/or towels.
So lately, we've been thinking about giving up the closet to a washer/dryer combo unit or just a dedicated dryer. We're leaning toward the dedicated dryer. Our clothes generally don't get THAT dirty that they need much more than an occasional spot clean or light rinsing. So we could wash them, if needed, in the sink and just toss them in the dryer across the hall from the bathroom.
If we really did need something larger cleaned, then we'd use the campground or laundromat facilities. But a clothes dryer on board would be handy. However, every time I broach the subject with DW, she's still reluctant to give up "her" closet, so I'm not sure if we'll ever follow through with the idea.
I just wanted you to know that you have company in thinking that a clothes dryer alone could be sufficient. I don't remember hearing from anyone on these forums over the years who has installed just a dryer. It's usually a combo washer/dryer unit, usually with an assortment of very mixed reviews.
My advice to you is that since you already have the dryer is to install that and see how that works out for you. If you feel you need the washer after that, then you can deal with that issue at a later time.
Good Luck in your decision, and please let us know what you decided and how it works out for you. :)
~Rick