Jimulacrum
Full House
In other words, his presence allows elements of both skill and chance to be factors in a game where both skill and chance are appropriate factors. I do not see the problem.It's potentially problematic in another way which does not have anything to do with emotions.
If the guy is truly committed to busting very early, this means (a) the game always loses a player early, making it shorter-handed than normal every week; and (b) he is creating a 2x stack on the table very early every game, which skews the early gameplay in a specific way (assuming the doubled up guy knows how to use it to his advantage).
Sure, that could happen naturally -- AA vs KK on the first orbit, etc.
But if it is happening *every* game then the reckless/suicidal player has effectively made a unilateral change to the format.
Another odd result of his approach: I assume that some nitty players are *never* calling his early all-in with anything but premiums... whereas a couple others probably realize that calling with any pair, any Broadway combo, any suited ace, or really just any top 25% hand is probably a good move if you don't mind leaving early roughly a third of the time.
In other words, the reckless player is gifting the thinking players with a giant new edge. Nice for them but again the reckless player has skewed the longstanding dynamic in a way which is more random than the host likes.
Also, I encourage you to read the OP carefully. Try to piece together a clear claim of what percent of hands he's really shoving, and as you find the conflicts I found, ask yourself if OP has taken a bit of storytelling liberty here. I suspect his play was far less than shoving literally every hand.