First of all the reason I didn't list Carter Hart is I don't consider him a valuable goalie asset at the moment. His game fell apart last season (arguably the single worst performance from a starting goalie this past decade) and I don't think he's done enough to rebuild said value. For what it's worth the Oilers were likely to pick Cossa if Yzerman didn't trade up to cuck us, so the team WILL spend the premium draft capital on a goalie if they deem them good enough. They just didn't like Wallstedt for whatever reason. Heck Rodrigue was a 2nd round pick and he's tracking worse than the lower drafted Skinner.
We've had many goaltenders this past decade flounder under Schwartz to go on to see success elsewhere. Dubnyk is the one that hurts most since he was homegrown. Cam is another player who came from New York and had a solid first 2 years here before falling apart under Schwartz and getting "fixed" by Calgary and Minnesota after leaving us. Brossoit isn't anything special but did carve himself a nice niche as a NHL backup which is more than what could be said about his tenure with us.
Carter Hart failed within context of an epic organization failure. One that cost two coaches and potentially scorched earth reality to reboot an impatient organization. His numbers though were better than the two year ago crash I think you reference. He's an established NHL goalie on a trainwreck team.
I don't recall Dubnyk being under Schwartz but do the prior former Team Canada goal coach. Regardless, he was sewered by a shitty organization too that was a systemic trainwreck. He also required multiple organizations to rebuild his game, technique and mental strength. If people believe in Skinner, it is easy to draw the conclusion that Schwartz has been a part of his development to NHL level backup. Goaltenders, as said before, are inter-dependant to the quality or not of team in front of them. Hart and Dubnyk perfect examples when the trainwreck is all around you, goaltending quality and results will be negatively impacted as well.
Oilers have failed massively in squandering the best draft collateral of the league for an extended period of time. Failing to address goaltending just seems to be par for the course of being poorly managed.