I disagree that Vancouver is in a bad position (at least for this season)...
Luongo fits under their current cap situation this year, so there is no pressing need to trade him today, unless its more an issue of resolving a potential issue dealing with team harmony/chemistry and distractions if kept..
Also Vancouver even in a shortened season ahead is still primed as a strong Cup contender, this being based on winning the President's trophy the past 2 seasons running as best regular season team.
So if Schneider fails/struggles or gets injured than Vancouver's Cup aspirations are flushed down the drain with that, if Eddie Lack is the only option.. Which makes Luongo for this season a really good insurance policy if nothing else with 2 NHL starting goalies in tow, and a really good idea for the Canucks. IMO
I personally would wait until this summer, or if a top team needs a goalie this year and is desperate to acquire Luo at a steep price, or I could get a return that helps my team moving forward this year (and beyond) with a better chance of winning it all before dealing him.
If Tyler Bozak who is a UFA at seasons end, and if he is the best piece that Vancouver is getting from Leafs then why bother unless dumping that contract at all costs is the real motivation here. If the situation were reversed here and Leafs were a strong contender and I was dumping a proven starting NHL goalie for spare parts to simply dump a contract, then I would be angry if it hurt the team and its chances this season for success.
Not sure how you don't see that Vancouver is in an undesireable position.
The #1 thing a GM DOESN'T need is other teams knowing you want to / NEED TO unload a valuable piece. This IMMEDIATELY lowers the value of the player in almost all cases, and here is no exception.
There absolutely is pressure to trade Luongo before the start of the season . . . from what Luongo has stated publicly, to Schneider's playing time, to Luongo's weighty contract, to Vancouver wanting to get the fullest value possible for him.
If they keep Luongo like you postulate, his market value drops in half, and of course the obvious, it's absolutely shoddy GM management of player contracts/value. One would only do that kind of thing in an emergency situation (ie a goalie loses his ability to play goal mid season). No way does Vancouver do that.
One must never, EVER listen to what public statements are made by both trading parties before a trade . . . at best, it's obfuscation; at worst, it's disinformation and outright untruths. And that's all fair and good, it's professional sports, so why would some dummy GM ever even hint at him needing to unload his star, big contract goalie? Why would Burke ever want to display the slightest hint of urgency at improving his goaltendign position? Of course they won't give the game away!
So please,
Give me your reasons as to why a GM would want to:
1) decrease Luongo's trade value
2) create dissent/confusion in the dressing room
3) slightly undermine your new young goalie's confidence by keeping the other starter
4) greatly increase the chance of horrible play from Luongo/further dissention by not trading him and keeping him as a back-up
Would you want Burke to do that? I sure wouldn't . . .