The most common example is a wall with a toilet drainpipe. In the US, that requires a 3" inner diameter pipe - the outer diameter is 3.5", which is exactly the same as the space inside a 2x4 wall, but if you need any fittings, it won't fit, and even if you don't, the likelihood of being pierced by nails is too high when the pipe is right against the drywall. If you have a single-story house, there would be no need for such a drainpipe, so this is primarily an issue in multi-story buildings. Sometimes there's a central chase that contains these pipes (as well as HVAC ducting), but unless all your bathrooms surround that central chase, you'll need a 2x6 wall somewhere.

As far as I know, no. I learned about this when I lived in North Carolina. The house I grew up in had 2x6 wet walls with all other walls being 2x4.

It could be state or local building codes based. Here is a mention of it from a city in Illinois. But it definitely isn't just a California thing.

https://elmhurst.org/DocumentCenter/View/1826/Plumbing-Requi...

https://www.reference.com/world-view/standard-wall-thickness...

> I've never seen a wall framed with 2x6s because it had plumbing in it. It's all 2x4 regardless, here—you almost never see a 2x6 wall. Is that a California thing?

My California home is all 2x4s everywhere and there's plenty of plumbing in most walls.