Hagg was birthed into the NHL by a coach who encouraged his defensemen to join in the play. It was no different than an uber talent like Brandon Manning constantly activating and generating zilch out of it, often getting caught in the process. Hakstol's favorites in particular had a lot of rope. So, what you're seeing is a player, with below average hockey sense and skill, coached to play outside his abilities to the point it's probably habitual. He's playing the way that led him to 2 NHL seasons. There's a fine line between freelancing and foolish over-aggression. Hagg has always been a player who has zero balance between passivity and aggression because he can't read a play.
The fact that the coaches are testing multiple skaters to replace Hagg, with Myers being the potential death knell, tells me they are likely not satisfied with Hagg. So, is it so implausible that in the video room they are instructing him to pick his spots better, as he gets burned for odd mans and goals against? I'll tell you what the simplest explanation is NOT: that the coaches are actually instructing the least talented defender on the team to jump up every rush and leave his offensive partner, Gostisbehere, holding his purse. The simplest explanation is likely: he had a 100% save% for the first couple weeks, and private instructions or not, they left it alone.