This definitely plays into the hand of greed. If you only bet 1% of your bankroll on each game, you would have to lose a shit ton to go bust. Unfortunately, 99% of the gamblers don't follow this strategy.
The BR management is only a 'problem' if one has the edge to be winning longterm in the first place. A typical losing gambler who is following the 1% rule would just slow down his demise.
But when someone trully has the edge, BR management becomes crucial. I've known quite a bit of "good" poker players and bettors who went broke just because they only had the knowledge and expirience, without having the mental toughness and discipline to absorb the inevitable losses.
Its a pretty tough area to get better at. Exprience helps, but in the end, some people just cant deal with the net loss and can not avoid chasing.