I have friends who are expats and they’ve done this for years. I had one family member who left every six months to renew their visa.
It’s a chore, but very common around the world.
In the EU you do not need to leave to renew your visa. I don't know how common it is elsewhere.
Sorry, but that is not common around the world. Most countries do not have such a system. I.e. none of the EU/UK/Australia countries have that.
Were the visas for the US? B1/B2?
I know stuff like this happens for digital nomads in southeast asia or Schengen but the US generally doesn't approve of "visa runs".