We just have the baseboard similar to your picture. IMO there's no need for shoe unless there's a gap to cover. It just introduces more caulk (they'll typically caulk between the two because they won't fit exactly) to maintain and the shoe is a dust catcher, especially if painted white. I insisted that they install the tile first, then put in the baseboard because in our previous master bath, they had put in the baseboard, then tiled up to it, then grouted in the baseboard. I did not like that look. Our builder said they do it both ways.

We just have baseboard (over the floor tile). Our molding is flat , all straight edges. It looks fine as is (IMO) as our style is contemporary (clean lines).

I think the shoe is sometimes used to hide any gap that may appear between the baseboard and floor as the wood of the baseboard shrinks due to seasonal variations in humidity. A wider base will shrink a bit more than a narrower one. So, depending on what materials are used and their dimensions, and whether it's all painted and if so how, this isn't an issue. That said, I have 5" wood base sans shoe and have no seasonal gaps.

A shoe can also cover less careful work. If the floor is new, it should be flat and baseboard scribing, which takes some degree of skill, should'nt be necessary, giving you a better chance that the installed base will be tight to the floor, no matter who's installing it.

I'd go without, unless your contractor has a good reason to use the shoe. Did an architect draw the plan? If so, maybe there's a design reason for it.

Thanks for the advice. I decided to go without the shoe molding. I think the designer put it in because he was worried about water/moisture in the bathroom but I like the look a lot more without it.

Where we have wood flooring, yes because of the gaps needed to allow breathing room for the wood. Where we have carpet and tile, nope, no shoe molding.