Has anyone here actually played sports beyond mites or pee wee? Are any of you older than Ovechkin and facing the daily bumps and bruises and mystery pains that come along with being an aging athlete? Have you been through surgeries or physical therapy? I think a few of you fit this description but I'm guessing most don't. It sounds preachy but unless you've been through these things you're just stabbing at the air with theoretical armchair analysis of things that really require day to day experience.
The modern approach is to keep active as much as possible and get active as soon as possible in order to retain strength and mobility/ROM. It's very hard for a professional athlete--especially a high priced team captain--to take time off to completely heal. Only during an injury's acute phase do you rest and hope to reduce pain and swelling. After that you may be impaired but you're still supposed to be active.
It's also very hard to distinguish between what's "Oh **** I need to stop and let this heal" injury vs the inevitable aches and pains that go along with the package. Some things go away, others don't. You can't just lie in bed all day for 2 weeks and BING your health bar is full like some video game character that's found a rest point. There is ALWAYS something wrong, and it's often hard to pin down.
It's not difficult to imagine several lingering injuries affecting Ovechkin all year, and then becoming magnified in the playoffs following the trauma of a hit like Kadri's. Having your knee joint bent backwards is going to put a violent strain on your opposing muscles, like the hamstring which may be fatigued or damaged from a long season. Playing on that for a few more games or weeks is going to impair recovery and make a tear more likely.