I think you're overusing the term "unicorn" as well as misusing it. Ayton is a skilled 7 footer but he's not a "unicorn". What makes players "unicorns" is that there are only 1 maybe 2 in the NBA today. If all of the guys you mentioned were "unicorns" then none of them would be, the term is used to describe a very unique combination of skills a player has that makes them a rarity in the NBA, 1 in a million type players. Giannis and Porzingis are the only players I've heard analysts refer to as "unicorns" before and with how they're built and their skills, it makes sense. Players with their physical build don't often have their skillset. Ball handling and speed of a guard, size and strength of a Center, agility and range of a SF. There can't be a dozen unicorns. Ayton is very much a Center, a very skilled Center, but a Center none the less. Also it's not money that has held up or forced any of the deals you've mentioned.
Money won't be why Towns is traded, like Phrazbit said above. KAT getting paid has to do with where he is in his career, and that's it. If you read up on the rumors it's said that Minnesota will fire Thibedeau and pay Towns to get him locked in. They don't want to lose him and they want to repair things before he is publicly demanding a trade. They're not thinking about trading him because of his contract though. Towns is upset about his role in Minnesota, it's not about money. He's not asking out because he knows he'll make the most staying put also. Minnesota will fire Thibs before they trade Towns and after they fire him, they'll roll out a max extension that he'll sign. It's not money holding things up there.
Also KAT hasn't taken Minny anywhere yet because he just finished his 3rd year, like Booker. He did help get them to the playoffs this year though and he's vital to getting them back there. It takes time to build a team and Minnesota is now trending upwards, they'll be better next year with everyone back. Like us, they just assembled their "Big 3" this last season, and they made it the playoffs. Our "Big 3" won't get us there next year but in Ayton's 2nd or 3rd year, we should be a playoff team. Putting our trajectory similar to the Wolves with KAT. Don't discredit what he's done. Players don't often lead their team to the postseason early in their rookie deals. Towns has 1 more year on his rookie deal, the Wolves are a playoff team now. Hopefully the same happens for us, maybe a little quicker.
Cousins was traded 2 years before he could be a free agent because their owner is nuts. He thought Buddy Hield would be the next Steph Curry and gave the greenlight for that deal with the Pelicans. He was on the block at that point because he had gotten 5 or 6 coaches fired through his first 6 years in the league and was seen as a headcase. They decided to move on while he had trade value before he was left with 1 year on his deal and they had less leverage to get a good deal in return. No one wants to risk trading for a star player with 1 year left on their deal, it's a huge risk and it gets GM's fired and sets teams back years if that player walks when they become free agents. Cousins is due a new contract but the Pelicans seemed content paying it before his achilles injury. That's a huge injury, as serious as microfracture. Only 1 in 3 players return to the level they were before that injury. I'd posted an article that number came form before and I can find it again if needed. No one will want to risk paying him max money because of the injury, not his skillset. If he were healthy, he'd get the max easily.
If your theory on paying bigs was true then Embiid wouldn't have gotten a max contract from Philadelphia before this last season after only playing in 32 games in 4 years. It was a gamble, no doubt, but Philly wasn't going to risk him walking or damaging their relationship. By signing him to that extension they protected themselves some because they were able to add in some injury clauses so they'd be saved if he ends up going down again. If he was a restricted free agent this summer, he would have gotten a max contract from someone without those provisions included so they made the right move, ultimately.
