What if you had a Lamborghini and tried to haul dirt with it?
The cup winning team is either going to have finished 11th best or 21st best in terms of goals against this season. Hardly defensive world beaters. The Oilers were right around league average in goals against with bad goaltending the majority of the year. There are plenty of ways to win in this league. You don't completely revamp how your team plays because you have a goalie who can't make a save. You go out and get a goalie who can.
Your analogy is altogether ridiculous.
A team finishing with the best goals against, meaning they excel at defensive hockey, would likely defeat either the team that finished with 11th best or the 21st best goals against,
particularly when the team giving up the least goals against also had the best power play in NHL history.
I'm assuming you don't assume the Oilers would be playing defense when they had the man advantage. I assumed you might think that the Oilers increasing their defensive efficiency would be a good thing.
Good defense leads to offense and the Oilers still have the two most offensively potent players in the league. Asking them to play more defensively aware isn't asking them to slow down, it's asking them to cut down on the goals against. They wouldn't have to spin their wheels while enacting a superior structure of positional defence. And they would still be skating on ice... not dirt.
Maybe they hustle to complete their defensive assignments negating high danger scoring chances against, block the passing lanes, and cause turnovers. Then when the team has possession the of puck they can go on the offence. When a team doesn't have possession of the puck they are more likely to get scored against!
Vegas scored as many goals as they needed to win against the Oilers. It is a theoretical construct that I propose the Oilers be the team with the least goals against. But it is a real world solution to the approach with which the Oilers can win championships, by playing better defensive hockey.
The Oilers problem is the Oilers can't play defence. If the Oilers refuse to play better defensively you'd have them play more offensively?