I don't like the idea of walking through the bathroom to get to the closet, though I've seen it done.

If your bathroom has a good fan, it should be ok.

You are describing my master suite. My shower head is fairly close to the door to the closet, and I must walk through the master bathroom to get to the master closet. Many of the houses in my neighborhood are like this. I don't think its a problem as long as you have a fully enclosed shower. (By "fully" I mean it has a door, and walls on all 4 sides of the shower -- I'm not talking about the shower being completely enclosed on the top. In other words water can theoretically splash out the top of my shower, and onto the carpet in the closet, but in practice it doesn't since the shower walls are quite tall (over 6 feet, I believe). The shower walls are pretty good at keeping water in.

This photo is fairly like my master shower. The shower head would be on the left wall inside the shower in the pic above. The door to the master closet would be just outside the shower on the left side of the pic, at a 90 degree angle to the shower door (the master bedroom closet door is on the same plane as the wall that the shower head is on.)

In addition, the wall on the other side of the shower head is inside the master closet.

Do you have the floor plan?

That said, I live in a very, very dry environment where moisture isn't as problematic. Here is the floor plan: https://www.richmondamerican.com/content/plans/jessica/42839_jessica_u290_1_14_16.pdf

Doesn't bother me.

It hasn't been a problem in my current or former home that had this setup. Lived in the former home almost ten years, current house has been six years already. The home we owned before that had a different set up. We rather prefer being able to go straight from the bathroom to the closet to get dressed... so long as the closet is large enough to do that in. I've always kept undergarments in drawers in the closet, we don't even have a dresser in the bedroom.

I also live in a dry climate and, although I’m not sure if that has anything to do with it, many houses here have the entry to the closet in the bathroom including mine. To be honest, it never even occurred to me to question it because I rarely see a house that doesn’t have that setup unless there’s no walk-in closet

I wouldn’t want it any other way. I live in a humid climate and have never had a problem.