While the specific value chosen will be brand-specific, you're right that this is common behavior. My Fujifilm point & shoot favored ISO 800.
Increasing the ISO from 100 to 400 doubles the effective range of your flash, which is important with a relatively-anemic built-in flash. It also means that half of the flash power can be used for a subject within the normal range, saving battery life, decreasing the time it takes to be ready to flash again, and shortening the duration of the flash pulse to better freeze motion.
Another approach would be to increase aperture (more open; smaller numbers), which would have a similar effect, but would reduce depth of field. That means focus has to be more dead-on, and is generally not what auto-exposure modes are programmed to go for unless they have no other option.
I don't know the specifics of the auto-ISO logic in your camera model, but I wouldn't be surprised if it favors keeping ISO at around 400 and only increasing it only when there's not enough flash power.
When I'm using off-camera flash, I usually set ISO manually, but I generally default to around 400, just like your auto mode. This gives me a lot of flexibility in aperture, and even though my camera isn't the latest sensor generation, that ISO is clean enough that I don't really worry about noise.