What does it mean that Arm is headquartered in the UK, practically speaking? What kind of a change would need to happen for, say, the Austin office to become the headquarter?

If I remember one of the original conditions put on the acquisition of ARM by the UK gov was that HQ stays in the UK. So I doubt that will change. Can't say I'm familiar with the tangible benefits, but I assume is exposes ARM to UK law and regulation more than if the HQ was in another country. And retains some jobs in the UK.

There must be some benefit for governments to make such a request.