It has been said the broader gauge was chosen at the time to make trains able to run safely over Golden Gate Bridge with strong side winds. My physics is not good enough to calculate whether that argument makes sense. And I have no idea how realistic that route ever was.

I don't think the gauge is a major problem. Train orders are always a custom project, few urban networks use exactly the same standards. Railroad manufacturers are used to different gauges.

In particular the track gauge is a long way from being the only consideration. Structure gauge and Loading gauge are also crucial. When I first moved here despite this being an important port city a Victorian arch bridge carrying road traffic over the railway meant every single freight train carrying containers from the port to the rest of the country needed to either go on a circuitous route or use special low wagons with reduced capacity, which hold a container below axle height so as to fit under that bridge.

In that case blocking the road and dropping in a new road bridge was affordable given the economic value but generally you put up with what you've got.

True, when it comes to loading gauge one can no longer even about a standard. Most countries have several different loading gauges even for the same track gauge.

In practice I am not convinced the BART is severely impacted by their "weird" gauge (whatever is meant by that, not sure what their loading gauge is, for passenger trains the distance to and height of the platforms would be most relevant).

Stadler KISS series used by Caltrain is built at least in 3 different widths.

Auckland, NZ had (not sure whether still in use) rolling stock from the UK, converted from 1435 mm to 1067 mm track gauge, the loading gauge obviously was close enough.

Finland has engines (Sr3, Dr20) and railcars (Dm12) designed for smaller central European loading gauges. They look a bit tiny compared to other stock, but they are fully usable.