He also is barely a net positive ES and is one of the worst defensive players in the league.
Not sure where this fallacy comes from.
But, without him, the Lightning would not have qualified for the playoffs this season. Absolute fact - one player really did drag the rest of his teammates to the finish line. The defense, including the contribution from the majority of the Lightning forwards, has been abysmal this season overall, and only until the recent stretch have they tightened up their game. Vasilevskiy has fiddled with mediocrity most of the season since returning from back surgery and definitely hasn't bailed the team out like he has in the past (except for finding his more typical game as of late).
The fact he's a winger yet still controls the play and runs the number 1 PP - he sets everyone up. The way he slows the game down, the passes he makes are unreal, all the backhand passes he makes. His teammates and opponents constantly mention his work ethic and how he's never satisfied and always working on his shot, his stickhandling, subtle aspects of his game and never leaves the ice. How his hockey sense is unmatched and that is what makes him great - not being the fastest or having a hard shot or all of those skill sets he admits he doesn't have or the "flashy" skills - but he makes up for it by reading the ice better than anyone.
Remember watching an interview with Bellemare where he mentioned how Kucherov would take these hard passes around back of the net and then immediately make a perfect backhand pass to Stamkos for a goal in front of the net during a game. And Bellemare would want to try it, try taking a hard rim on the backhand in practice and could never control the puck to make a surgical type pass like that, that the puck just exploded off his stick and went wherever yet somehow Kucherov controls it and delivers it exactly where his target is.
Yeah, I'm biased, but his game is seriously underrated and underappreciated. He's the ultimate team guy. He deserves the Hart.