The only two things that bothered me with Conte are your last two points. Bitching via media is fine if you do it in certain volume, but he overdid it completely (I also severely dislike Mourinho, Wenger, Benitez and Garcia for this kind of stupidity), and became directly confrontional with the management almost. His hot blooded and impulsive nature took over pretty much. The way he left, yes, thats pretty much a stain in his stellar and legendary work with us both as player and coach.
The tactical stuff, it annoyed me how set he became in his ways, but the results speaks for itself in how pretty much dominant we were with it. So he was doing alot of it right, its just lacked the flexibility to adapt to different scenarios, thats all. I can accept that.
The CL thing, total BS for me, he became too self-absorbed and defeatist in attitude latter on, but I would say its just circusmtances, it happens, part of is tactics, but we did very well in first CL season, 2nd one was just unfortunate mess, and not a overall stain in his ability as coach. Seen top teams struggle in group stages before (especially ones that have the mental handicap in Europe as we do, plus inexperienced squad in this level, and yes also a young coach who refused to adapt tactically to this stage). The main issue with that was the pressure he himself and the club set on itself for Europe. Became almost self-fullfilling prophecy, to talk the talk at first, then play down the shortcomings and talk about how far we are from the rest of the big guys (main culprit is Conte, his ego/personality is a hard one in this way). But performance wise, we were pretty average/mediocre for most of this CL season too, struggling vs Greeks and at times Swedish amateurs (for 70 mins, took a Carlitos who finally woke up in Europe). We just learned from it and got the job done eventually. Just as we did in first CL season. Allegri is more experienced coach, but its kinda silly notion to say he is better CL coach just because of last seasons mess.
Main and only issue with me with Conte remains the huge gulf in goals and ambitions there was with the management enough for him to not be able to work with them anymore. Rest of it is just gravvy. Allegri is doing well considering it all, but never forget who laid the foundations for this well oiled machine, very ideal set up for a new coach to take the reigns in IMO, even if I notice and appriciate the changes Allegri came with alot. But end of the day, the differences in the coaches remains for me, and that is if Conte was able to set his stubborn personality and somewhat of an ego aside, and come to understanding with the goals of the club/management, then yes I would fucking LOVE to have seen him remain at the helm, it still kinda hurts to not have him here, at least for me. Maybe not for most of you who somehow grown to dislike him so quickly, even if yeah how he left is VERY disagreeable, it doesnt change as much as most of you pretend it did in terms of what he was part of making.