I think there's still a lot of inputs that need to be added before something like this can work well. How fast the shot is, how long the shooter had had the puck, how fast they're moving, if they were passed the puck where did that pass come from, etc. How soon we'll have tracking data with that sort of specificity is way beyond my area of expertise. What xG might be in the future isn't really relevant to whether or not it's a useful stat for this conversation, though.
I'll defer to your assessment of how the Lightning play, but I will say that as a lifelong Caps fan, I'm intimately familiar with how an offensive system and individual players can succeed under regular season conditions but wilt in the playoffs when teams play harder and adjust to systems over the course of a series. I can't pretend that I know hockey well enough to identify what translates to the playoffs and what doesn't (I first got into advanced stats because I've never been good at seeing the bigger picture while watching the games), but the 15-8 margin at 5 on 5 in last year's playoff series is obviously a point in the Caps favor in that regard. My guess is that the Caps' size/speed combo and defensive system allowed them to wear down the opposition over the course of the series. They were a combined 7-1 and outscored opponents 19-12 at 5 on 5 in the games 5-7 of their various series (+0.88/game), compared to going 9-7 and holding only a 33-27 margin at 5 on 5 in games 1-4 (+0.38/game). Yeah, it's a small sample size to draw a conclusion from, but it's better to make conclusions from small samples than from larger ones that might not be representative of what you're trying to assess.