Long story on what the ISAF thinks, they say you cannot call it a "World championship" unless they endorse the event. they will only do that for certain classes who meet minimum requirments. In return, you get to use the rules that we all know and love.
As for the "Little Americas cup" moniker. That's another kettle of fish. It was a nickname coined in the 60's that followed the ICCT which was sailed in C-cats. It made sense because the same kind of intensive design development went onin the C-cats as did the AC ajnd they both ended in match racing events so it was a clos analoge.
Well the c-cats didn'r race for a while so Seacliff YC the holder of the ICCT deed of gift chose to run the event in HT18's or whatever boat it is today and "retained" the moniker, "Little Americas Cup". Many would argue, including me, that it's not right and that should be accorded to the c-cats. Now the AC management has wadedin and said nobody can use the Moniker "America's Cup" in anything anymore except for them.
Personally it doesn;t make a big difference to me but for teams who need to raise funds to compete through sponsors the name would presumably help a lot. A positive brand association as they say in the business. ACM would call it a copyright infringment.
don;t ya love politics?