"Cotton's naturalisation attempt was not treated with the urgency necessary, if he was to be available for selection to the Boomers. BA could not guarantee that Bryce would be the one, allowable, naturalised player because of the availability of Mattice Thybulle."
Cotton got bad advice and tried to get qualified quicker using the DST visa which has a really high threshold that he was unable to meet. One of those requirements, yes, is that he's an obvious no brainer pick. With Thybulle that was never clear cut.
"My question is; Wasn't Mattice born in Aust (Melb) and consequently Australian-by-birth? Meaning, he did not need naturalisation. He will always have been Australian-born. I can't see why we could not have had Bryce and Mattice."
No Thybulle was not born in Australia. He lived in Australia for some period after which he qualified for citizenship. Typically if a player receives citizenship when they're still a child they don't end up a restricted player (ie the one naturalised player per team rule) so I'm not sure on the exact situation for Matty as its clear FIBA consider him to be a restricted player. As such with him and Bryce it would always be one or the other.
"Kyrie Irving is another example. Seems that he can play for Aust. (Yes, there are other reasons why Kyrie may not qualify). Could that turn out to be 1 of the 3, or if all of a sudden, Bryce, Mattice and Kyrie all became Boomers (in place of say Delly, Patty and Sobes, from the current Roster)?"
Kyrie was born here and received Citizenship as a natural born citizen. He has since chosen to represent the US which means he can't play for Australia except if given special exception from FIBA which almost certainly (and rightly) would not be given.
If all went as planned (Bryce became Aussie, Kyrie never represented the US) we could have 2, never all 3.