Last euros was more than a year ago. Chiellini was even better then and he's in MLS now. Nations league was 2 games, hardly a sample size. If you wanna use them then also use the game vs Argentina few months ago. At his best Bonucci was a decent defender too, not only a ball player. But he looks finished and caught off guard and out of position often. He's slowing down physically as well. He's way past his best days and I struggle to see us doing well with him as a permanent starter going forward, no matter the coach.
You might want to know what you're talking about before you speak. We held majority possession against Salernitana and the play was most in their half, yet we conceded 2 goals with Bonucci playing. Against Monza he didn't play, we were with 10 men most of the game, Gatti lost his man on 3-4 occasions before the goal already, and we still "only" conceded one. Maybe if he was someone that can command a defense? Which a defender of his experience should be able to do by now? Maybe we wouldn't concede 4 out of our 7 on Serie A with him as opposed to 3 without him (even if his alternative are Serie B Gatti and Rugani), and all of our 11 in the CL with him vs zero in the 67 minutes he didn't play? His ball playing isn't as necessary when you play AS, Bremer, Danilo together, all guys that can pass and dribble forward. Only thing Bonucci has which they lack is the long ball, but there isn't that much space upfront now and quick strikers to exploit it so it's redundant.
As for your struggling to keep possession argument, hard to do so with McKennie and Rabiot as mezzalas, and our 2 creative wingers playing less than 3-4 full games so far combined. You can blame that on Allegri for not trusting guys like Fagioli or Miretti enough over a barely footballer McK, or not giving Soule enough chances when Kean plays every game, that's fair. His player selection is one of the main points to criticize him on. But once guys like Rabiot, McKennie, Kean are on the pitch already, and you expect them to play quick one twos, or to create space for Kostic and Cuads on the flanks to exploit, well, you're setting yourself up for disappointment