There's really no way this can end well.
The drama surrounding the Phoenix Coyotes has been going on for months. It's almost certainly hurt the morale of the team, and it's been terrible publicity for a league that already struggles to maintain credibility outside of the Canadian market.
Part of establishing that credibility has been trying to prove that hockey is a sport that can be universally appreciated - and to some degree, they've succeeded, with championship teams in Raleigh, Anaheim, and Tampa Bay. Sports that can't have a universal appeal will always be regarded as niche sports.
This is not to say that Phoenix is a good location for a hockey market. On the contrary: Arizona, on the whole, is a terrible market. It's a state with a tiny population and sports teams in all four of the major leagues - a recipe for disaster, as the only sunbelt teams that have succeeded so far are those in major metropolitan areas or cities without other major league sports teams.
But it's not impossible that the team could be made viable, and given an objective approach (absent the passions that understandably run high when discussing the possibility of another Canadian team), it can be shown that it's organizationally better for the league that the Coyotes stay put - for now. Buffalo and Pittsburgh were both targets for relocation, and both teams have rebounded from their darker days.
There are two likely ends to the situation surrounding the Phoenix Coyotes.
The team is kept in Phoenix. Their future is uncertain, and the NHL has to suffer through the public embarrassment of having to fight to keep one of their franchises from being relocated due to bankruptcy. Even given future success in Phoenix (which is a long shot), that stigma will be difficult to live down - and if they are forced to relocate later, the embarrassment will only be increased.
Balsillie gets his team. I foresee a lot of owners refusing to deal with him because he circumvented them to get into the League, and possibly a wider-spread crisis as the league uses every legal tool in its arsenal to keep Phoenix / Hamilton from playing. It's reasonable - there's a front door into the NHL, and Balsillie didn't use it. Being a ruthless businessman does not endear you to people.
In addition, Buffalo gets 12% of its season tickets from Canadian residents - and I expect that number would drop significantly if a team was placed in Hamilton, as well as merchandise / ticket revenue. Long-term, that could result in the folding or relocation of the Sabres depending on how severe the impact was, giving a major black eye to the NHL.
My unpopular opinion
One only need look at the TSN website to see how viciously anyone that defends the NHL is getting attacked. It's understandable - Canadians want another Canadian team, period.
But look at it from an organizational perspective. Allowing someone distrusted by every sports owner that's ever dealt with him into the NHL through a back door is a recipe for disaster for the NHL, and the long-term ramifications of Phoenix moving East could hurt the NHL. While Bettman obviously has his own interest in keeping the Coyotes where they are, it's better for the NHL that they stay there than move to Hamilton.
This is not to say that there's no avenue for them to be relocated later - however, if they are, it needs to be in a controlled, methodical manner, in order to mitigate the stigma of relocating a team; rather than frantically moving a franchise in trouble, it needs to be a careful process involving the league, not circumventing it. Yes, everyone is aware that Gary Bettman is Public Enemy no. 1 in Canada, but trying to blow him out of the league by destroying his sunbelt plan is useless if you damage the league in the process.
It's indisputable that Canada, as the cradle of the sport, deserves another hockey team.
But that extra team can't come at the expense of the sport itself.