Rest rooms aren’t so much designed stronger for storm purposes as having common qualities that make them suitable. Since you’re from California I’m sure you’ve heard about standing under a doorway during an earthquake - it’s not that doorways are explicitly designed as earthquake shelters, but certain inherent qualities of doorways make them safer than some other places you could stand.
Rest rooms tend to be small, with close-in walls and few or no windows. These are all qualities you look for when taking shelter from a tornado, which is mostly what you need “storm shelters” for in the Midwest.
In the building I work in the employee break rooms and meeting rooms double as tornado shelters. So that’s what they’re used for when not sheltering people from tornadoes. They’re built like cinder block bunkers embedded in a larger, warehouse-like structure. The public usually never sees them, but I know of at least one occasion when all the customers as well as the employees were herded into those rooms (as it happened, the tornado missed the store but cut a hole through a mini-mall nearby).
If, for some reason, I couldn’t get to the back of the store and those designated rooms my second choice would be the rest rooms near the front entrance.
Tornado shelters don’t need toilets or food supplies - you aren’t in them that long. They don’t need to be spacious - you just cram everyone into the space for the short period of time you need it. They DO need to have very strong walls and no windows to protect you from flying/falling debris. If the ceiling of the main building comes down you want some chance that the shelter’s walls will take the blow and protect you.
That’s why something like a meat locker can provide protection - it’s a box (the meatlocker) within a box (the main store), no windows, no long span of ceiling overhead, no windows… That’s why basements work - the storm and the debris have to tear up an entire building before getting to where you are, and that’s unlikely (although, unfortunately, not impossible - all bets are off with an EF5). That’s why rest rooms work in public places - small, close set walls which are structurally stronger than large, open spans, no or few windows, etc.
One of the other reasons would be that communal restrooms tend to be permitted for use by anyone in the building, and often don’t require a special key to get in (if they do, multiple people will have one). In an emergency it’s probably best if you don’t have to ask for permission to enter a room, hunt down a key or wonder if you’re being terribly rude by encroaching on someone else’s space, delaying your access to the space.
If you’re stuck in a room for even a couple of hours having access to a toilet would probably be good for everyone involved.
As I’ve mentioned, that sort of storm shelter in the Midwest is generally for tornadoes. You won’t need to be in them for hours. 20-30 minutes at most, often less.
The wet wall usually uses 2x6 construction instead of 2x4, so a least 1 wall in the bathroom is thicker. I don’t think a few copper or pex pipes and an abs drain pipe play much into it.
Hallways also fit the description. And around here, most buildings seem to have an interior hallway (i.e. no windows) on the 1st floor designated as a tornado shelter area.
Where I work, the produce cooler is a tornado shelter.
Another reason for designated shelter rooms is so that emergency crews know where to hunt for survivors. Being “safe” under a table and a few tons of rubble someplace out of earshot doesn’t help much if nobody looks there for you.
I just passed through the Denver airport, which I rarely do, and noticed that all the restrooms are indeed labeled as tornado shelters.
By the way, the current advice on earthquakes is NOT to shelter in a doorway–because the door may swing shut and injure you. Best places are in a room with nothing that can fall on you (maybe a hallway), center of a room away from falling furniture or wall-mounted pictures etc., or under a piece of furniture like a desk or table.