Not sure about that, I think the AFL in particular are happy to let the FFA use the word "Football" whilst using and flogging their own "AFL" branding everywhere.
The AFL certainly aren't "happy' about the FFA trying to monopolize the word "football."
The AFL branding is mainly just that - branding - making the brand strong.
If the AFL want to use and own the word "Football" in Australia they would.
The AFL talk football all the time. Australian Football talks football all the time. They're all _name_ Football Leagues,
Otherwise we'd be watching the AAFL - the Australian AFL.
We probably should be calling soccer Federation Football as that is the title soccer has chosen.