That's all baseless conjecture, if you ask me.
There's a lot of noise about Irsay being a troublesome owner, but there's zero evidence of that. He doesn't meddle, he's well respected by everyone who's ever worked with him, and he (mostly) hires good people and lets them do their job.
If you have a problem with the owner of the team addressing the media about a very news worthy event, then that's a "you" problem. He's the owner, he can address the media whenever he wants, and usually when he does, it's to sell his product -- the Colts. That's his job. If you find that embarrassing as a Colts fan, I think that's something you're going to have to work through on your own. The owner is going to speak publicly.
It's obvious that he has personal issues, but it's a little unfair to always resort to his past issues with drugs. The way he's moving around, it's obvious that he's in a lot of pain, which kind of suggests that he's not using anything. He's not a good public speaker, but that's always been the case. Just because he says 'um' and 'uhh' a lot doesn't mean he's high.
And suggesting that the man who extended Grigson and Pagano and gave them both more time than almost anyone in the media or fanbase thought they deserved... the same man who took a full three weeks to fire Ryan Grigson ... the man who is now allowing Chris Ballard to take his sweet time with this very momentous coaching search ... has become impatient? I think that flies in the face of reason. Irsay is painted as this impetuous and unpredictable man, and that's largely based on some issues in his personal life, but it has zero to do with how he runs the Colts.
As for Nagy, that's just a difference of opinion. Suffice it to say, he wasn't very high on my list. And if he didn't like the fit with the Colts, it's a good thing he chose Chicago, because Irsay isn't going anywhere, and I don't think Ballard will be leaving any time soon either.