Fix: Power BI - Couldn't publish to Power BI

I saw the above message when working with one of my clients today. The error says Only users with Power BI Pro licenses can publish to this workspace. And that would make sense if they hadn’t already purchases Power BI Pro licenses for the user.
I checked online, and there were a number of comments about people seeing this error. There were the usual suggestions of logging out and back into Power BI. There was even one who’d quoted a Microsoft support person who said that Pro licenses don’t work for up to 24 hours after you purchase them. (That sounds dubious to me).
We checked that the license had been assigned to the user. I was concerned that perhaps the licenses were purchased but not actually assigned to the users. All was good with the license assignment.
But then we noticed something odd:
Note that the user still had their Free Power BI license assigned to them, and for some unknown (and not very sensible) reason, that was the one that the system was using when they logged in.
We removed the free license assignment and all was then good.
I hope that helps someone else.
2020-09-07