Why does Kyrie deserve say in Lue's hiring? He was -- at the time -- a 23 year old who had led a couple of 19 win teams. LeBron's arguably the best player of all time. There are very few players in the NBA who earn the right to have input on coaching and personnel decisions. LeBron is one of them. Kyrie's not.
As for Thompson, that's another example of your bias being revealed. It was all the rage back when that deal was signed to blame it on GM LeBron and laugh at how big it was. Of course, the next year the cap jumped by 40% -- something the entire league saw coming -- and Thompson's "above market", "tax crippling" deal that was a favor to Klutch sports or whatever is now the 61st largest contract in the NBA. He's paid less than Greg Monroe, Enes Kanter, and Ryan Anderson. He's the 18th highest paid big man in the league. Oh, and he was a key part of their championship, he's a perfect big for the modern NBA, and is
really, really good. The Cavs do not beat Golden State without Thompson's rare ability to corral guards in the pick and roll and protect the rim and rebound.
Which means that LeBron's worst issue as a "GM" is that he brought along his friend, James Jones, who is uniformly regarded as one of the best guys in the NBA. And if he'd kept open that roster spot, they'd have had a different 11th guy off the bench.