Well you could say they shut down Kane, after he was useless.
And they sat out Nurse for the rest of one game when he couldn't continue.
Draisaitl had a couple of issues (can't do much about broken rib).
McDavid's sounds like the one Backlund had that took him out for 6 months.
I think you would be hard pressed for the team or the player to sit out the playoffs.
You get close, this may be the only chance to ever win the cup.
Concussion? Sure, you sit out. There is set protocol for that and teams would be careful in their liability.