People who don't get carpeted bathrooms, underestimate the dangers of slipping on tiles.
It's no coincidence that the elderly love a carpetted bathroom. It's less of an issue than it once was, especially if you can afford a cleaner who shampoos the carpet once a week.
If elderly people tripping is the biggest worry than instead of carpet they should floor it with outdoor decking vinyl or something. Waterproof and gritty for grip.