Right. They don't care. They'll say they do, but it's a fairly minor consideration. Most people once they grow up their priorities shift to family (if they have one), career objectives, and money.
Even if you grew up a die hard Leafs fan why would you want to join the organization with this dysfunctional management? I'd rather go somewhere I have a better chance to win, where I'm paid more, and it would be nice to go somewhere hockey players aren't recognized in public too. Toronto is where I'd want to go to raise kids and retire though, that's why over the years we've been good at attracting veterans who are winding down their careers.
I'm not saying it would ever take priority over things like family and to an extent money, cause even if the Leafs were a stellar winning organization, it likley still wouldn't for many players. This doesn't mean that they don't care, and I guarantee some care a good deal. Also, not everyone wants to avoid the spot light, some chase it.
You stated the problem though, players don't want to come to a dysfunctional organization in general so the smarter young players are smart enough to stay away from a team they could likley piss away their career playing for. Look at Kessel for example; this guy could be the Kane or Carter on the Hawks/Kings, winning 2 cups and having many deep runs. Instead he's taking **** from fans and media for failing to make the playoffs (after scoring 37 goals and PPG) because management decided to build a team around him.
When we actually get a good young team, then we will attract all types of players, including those home town players who see an opportunity.