There have been no rugs in any bathrooms in my house for the past 40 years. Folks are getting SO picky now. I grew up in a house with a communal cup in the bathroom that matched the soap dish. Unsanitary. Then I was warned bar soap is also unsanitary so liquid soap that everyone pushes the same dispenser is better. Now I read cloth towels are gross and full of germs. Rugs are a trip hazzard.

We use bathmats in front of each sink. That is it. I do not like standing on cold tile when I wash up. They get washed every saturday.

Since you have marble slippery like ice bathroom floors you need a bath mat with non-slip backing, but a low pile that can be easily laundered and hung to dry due to the backing. So you need at least 2. Dry yourself and your feet thoroughly after bathing. If you still need a rug by the vanity buy a 3rd or 4th rug. As for the powder room, hang towel right next to the vanity so no drips if people need to reach for towel with wet hands. I would check with flooring person to see if PR floor needs a heavier finish to avoid drip marks.
No rug near the toilet ever!

We have a mat outside shower door and a runner in front of vanity.

I’ve seen a number of posts here with the basic advice that one should not have rugs in bathrooms other than in front of the tub/shower.

No, no, no. Solid no.

This is the Pinterest-effect, the idea being "look at my gorgeous floor, perhaps with a pattern -- I'd never cover it up with a fluffy bath mat, as this is all about the look". But bathmats are practical -- they're warm underfoot and they absorb water that otherwise would become a slip-hazzard.

No, no, no. The most solid of noes.

Then I was warned bar soap is also unsanitary so liquid soap that everyone pushes the same dispenser is better. Now I read cloth towels are gross and full of germs. Rugs are a trip hazzard.

Common sense says nothing's wrong with bar soap or cloth towels.

BUT as my grandmother neared 100 and fell on a regular basis, her doctor instructed us to remove throw-rugs from around the house. She didn't like it, but we did it.

That is it. I do not like standing on cold tile when I wash up.

Totally agree -- I don't particularly like my tile floor because it is So Very Cold underfoot. I much prefer the linoleum in my kitchen. Everything expensive isn't automatically better.

Additionally, I do not like stepping out of the shower and creating a drippy floor, which I will soon walk through in my sock-feet.

I wear slippers, and leave them near the tub/shower so that I can step into them as soon as I emerge. I have different pairs for cold, medium, and warm temperatures. My summer slippers are basically flip-flops with a contoured bottom. If you choose a washable terry cloth slipper you can put it on when your foot is still wet from the shower.

I have a rug in my bathroom, but I have no males in my household and no bathroom designers in my circle of friends. I don’t have small rugs in my house because they can be a tripping hazard, plus they’re always getting rucked up or out of place.

I was warned against marble for bathroom floors because of the slipperiness. If you don’t wear slippers you need a rug (or two, because when you wash them they take forever to dry) with a non-slip backing. Other than that, the only thing I can think of is un-polishing your marble, which I doubt you want to do. (I know of people who have had their countertops honed after installation — no idea if there are people who hone marble floors.)