Because the term "football" can have different meanings depending on where you are, but the term "soccer" is unambiguous and known to everybody*, it would make sense to exclusively use the term "soccer" when writing for an international audience, no?
It's ironic that in a dispute over correct writing, you've split your infinitive. "Properly to play" or "to play properly" are correct English grammar.
Just because a couple hundred years ago, the British had a Latin fetish and tried to shoehorn in new rules doesn't mean anyone should ever follow them.
Yeah, this is an odd quirk of some British grammars that wanted to imitate Latin. It's not an actual rule, and those grammars have been retired long ago.
Don't worry, some stuffed shirts made up the rule wholesale in the 1830s and a particular kind of pedant has been pushing it ever since. It's never been true.
