Friends had some of that cushioned sheet vinyl installed in their kitchen. When they moved the refrigerator back into place, they tore the brand new vinyl. So, yes, it can be a problem. Have to be extra, extra careful. And then I would be worried about moving the W/D later because the feet would settle into divots in the flooring because of the 'cushioniness'.

I just redid a tiny laundry room this summer. Basement; concrete floor. I ended up painting the floor. Wanted some color, too. Chose a bright pure aqua (no gray, muddy tones)... PPG's Breakthrough paint in Isle Royale. The paint store people told me that the local paper mills use it on the floor where there is forklift traffic. Dries super fast, very block resistant. About a week to fully cure. Also used the same paint in a different color on some closet cabinetry that I built for the basement.

(I'm use some of those interlocking foam tiles in front of the w&d in the winter because the concrete gets very cold.)