It was close to 10 years ago we did this.
The reason why passwords work better for us here is that we can arrange a class for paid members, several classes each month. The instructions and curriculum will be in private/locked forum. This will change every month and we will have multiple classes each month.
If we can simply add a password, we can email that out to the class lists. Using private groups someone would have to modify all those users and that is time consuming. Also what if a person pays for 2 of the 4 classes offered, how would groups handle that? The user would have to be a member of multiple groups. There will be new offerings every month so the list of groups would grow to an unmanageable task.
It may have been a mod I did to allow the passwords before, I don’t remember. This was long before WordPress.