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I'm also still not buying the 'washers need to be cleaned' theory. Our washer is probably going on ten years old. We have never taken any steps to clean it (outside of it's normal duties). Even with this lack of care on our part, the washer doesn't smell or have any recognizable 'growth'.
It should be noted that my wife had informed me that some HE washers need extra care to keep mold from growing in them. The tiniest bit of internet research leads me to the conclusion that this mold is caused by the fact that their doors close too tightly. The issue can be managed in a few ways such as 1) leave the door ajar (This would not work in my house as one of my kids would lock the other in the washer and probably turn it on.), 2) occasionally wipe down the door's seal with a bleachy product (it's the door seal that gets funky because it isn't washed every single time that the washer is used), 3) use the washer frequently. (We had six kids in my family. There was not a day that went by that a load of clothes wasn't being washed. There would be no mold in our washer, if HE washers had been the norm way back then.) That being said, the public washers at the resorts get tons of use. I seriously doubt that they have much time for their to be mold growth in them.
It should be noted that this mold growth on the door seals of some HE washers does not mean that these washers do not adequately rinse away whatever funkiness was washed off the clothes. I'll not stress one moment over the possibility that some minute particle of some previous wash remains in the washer. The only logical conclusion to such worry is to NEVER use a public clothes washer since you will never be sure of what was washed by previous users.
This isn't technically on topic, but I wanted to respond as someone may read and think all of your post is accurate.

I own an HE washer, and your ideas, while likely well meaning, are not factual.
HE washers often end up with a musty smell in them that CAN be helped by leaving the door open at least part of the time. The rubber gasket around the door seals so tightly it traps water and fungi can grow. But not all the fungi is relegated to the gasket area - there is a trap under the drum that has to be cleaned out periodically, and believe me, this thing is pretty nasty!
It has absolutely nothing to do with a lack of water being flushed through the system, in fact it seems the more the washer is used the quicker the build up. I use my washer many times per day, and we have to clean the trap regularly or our towels start to smell funky.
You posited the idea that a funky smell does not mean the washer is not rinsing properly, when actually it can mean exactly that!

With front load washers, the clothes end up simply tumbling, rather than dashing in the water and if the trap is clogged, the water can back up.
Just thought I would clarify this a little bit for anyone reading along. I don't mean to belittle you in any way, and agree with some of what you've posted.
When my children were little, I used a combination of disposable and cloth diapers, and it was far enough in the past for me to have been considered "kinda weird" by my friends and relatives.

I sometimes dumped the solids *from disposables and sometimes not, depending on when and where, but I was the only one I knew who did. However, I always used disposable whenever traveling, I can't imagine trying to deal with cloth in that situation.
And I have to agree with those a little skeeved out by the idea of dirty diapers washed in the sinks.

Just as I was when I heard the tip given by an airline attendant to wash out your undies in the coffee pot.

I will still use the sink, as I believe it is washed well enough by constant use - but I'll never use another in-room coffee maker!
*oops, left out a critical descriptor!