I wonder if it would really get as much water out that you want it to?
Don't they leave mops fairly wet still, so they can mop the floor some more?

I was thinking with the spinner thing, according to the video it only takes a couple minutes so even if it bounces around you could steady it for that short time.

But the guy doing his shirt only took a minute and his didn't seem to bounce around. Maybe the one you saw was a very unbalanced load.

What I do for delicates is wash in the bathroom sink then toss into the tub/shower rinse it with the shower or tub faucet -or if you have a hand held shower sprayer that is even better - great for washing the dog too!

then to get the extra water out i do a simple squeeze then roll/fold it in a towel {still in the tub} and step on the towel to absorb the excess- or if a lot of water is still in the clothes it drains out and you may have to do it again with a second towel..

Saves on wringing /squeezing but then you have wet towels to deal with.
Our washer/dryer is right in the bathroom so it's easy to toss the wet towels in.