My neighbor across the street has carpet in his garage. Not squares but rolled out 15' wide material. Not sure if it is glued down or not. Was kind of shocked when I saw it because he keeps his car and gas cart in it. As strange as it seems it barely has a mark on it and he said he just keeps it vacuumed. When I asked he told me the original owner left it (it's been over 10 years). I recently had epoxy done and it's beautiful and when it was put down it had triple anti-slip put on it but when it gets whet it's still like a slip n' slide. In fact, when are dryer is running I sometimes find it a foot or more away from the wall as it line dances down the floor.
The washer doesn't have that problem because it is much heavier.
I had my driveway done as well (not epoxy but stain with clear coat and 2x anti-slip) it too looks great but it's also quite slippery when wet and it's a pretty steep incline as well.
Another option for the garage are those rubber garage tiles. Was looking at them as well but the "good ones" were actually more than epoxy.