Dude, I know you're a Coyotes fan. I know you watch the games. This sounds like it came from a jaded Leafs fan who thinks that Arizona should just get moved to a good ol hockey loving place like Quebec already. Chychrun absolutely gets top minutes, does face top competition (admittedly not as much as others but he still does) and he gets tons of PP time because that's part of where he's good. I'm genuinely not sure how you even came to these conclusions after being a fan of the team.
In terms of ice time, he's 32nd in the league and 1st on the Coyotes in how much he gets, he's at 38% of possible ice time. Makar is 1st at 44%. He's 19th at EVTOI/GP, 30th at PPTOI/GP. He sees tons of time on the PP, being 23rd at 64% in percent possible ice time. You are correct that he spends very little time on the PK, but given that he spends a lot of time on ice during OT, I don't think that's a clear indication at least of his defensive value.
Offensively he's 23rd in On Ice Goals%, 31st on Corsi, 42nd on Fenwick, 2nd (1st being Ghost) in Off Ice expected Goals For (meaning the team scores much less when he's not on the ice), 7th in Expected Goals,
Combine that with age and contract and it's easy to see why GM's want him. Like it are not all of those stats are indicative that he has 1st pairing value and is a top defenseman.
All of this should be evident if you watch the games, since when he plays our offense runs through him and Ghost and that's not surprising and he gets plenty of time on the PP and ice in general.
Whether or not BA is f***ing up by not settling for less is a separate discussion, but Chychrun is absolutely a top pairing D and very good on the PP and at even strength.