Just to start off, he's a 50 point top end offensive d-man who plays among the most even strength minutes in the league and does it to good to great effect. That sentence alone should be enough to kill the discussion. Gardiner plays the most minutes for us, and with Gardiner on the ice we are a winning team. That's pretty much irregardless of who his partner is, or which forward line is on. The only time he has struggled has been when he's been put in a clear cut #1 role.
As for his defense, he does the above while being on for less goals, less scoring chances, less shots against. With him on the ice, we keep opponents to the outside well, we protect the slot well, and we prevent zone entries well. It's kind of amazing that for year after year, Gardiner plays big minutes and the opponents just can't seem to score much against him, despite him being a "complete and total tire fire defensively", eh? That's kind of like saying that a perpetual 60 point forward is actually completely inept offensively.
Next thing, if you use what micro stats are available as a proxy for how many plays he makes, he is almost in the same percentile there as he is in arena-adjusted turnover rate. Which basically means that he doesn't even turn it over more than average player per play he makes. So then you'll probably say that his turnovers are much worse, as people often say. But like I noted above, it doesn't lead to opponents getting much better chances so either the turnovers are not quite as bad and numerous as they seem, or they disappear in a sample consisting of much more good plays.
Fourth item, players with no hockey iq don't reach NHL as anything else than fourth line enforcers. People with below average hockey iq doesn't become influential players. So yeah, he's soft and he makes dumb mistakes. That's an argument for him not being perfect, not for him being too bad to play in this league. And we all know he's not perfect, we all see him making mistakes and playing soft, and we all know that his bad games are worse than most players. But his average game is also better than most, and that's what counts.
Oh, and as a final point. The Passing Project showed some of their work on twitter not long ago. Gardiner showed up in several categories as one of the most effective passers among d-men in the whole league. He's got more qualities than just his skating.