I don't think Ovechkin taking so many more shots is a bad thing. It's not like a strikeout in baseball (when that unquestionably puts you closer to ending the inning, and the game). If Ovechkin can generate so many shots, good for him - I don't see that as something that hurts his team.
Let's compare him to, say, Steve Stamkos. From 2010 (his sophomore season) to last year - Stamkos was a far more efficient shooter (17.3% - by far the highest among any player with >200 goals - vs Ovechkin's 12.8%). They're surprisingly close in goals per game (0.58 vs 0.55) but Ovechkin averaged way more shots per game (4.5 vs 3.2). Clearly, Stamkos is a more efficient shooter. But ultimately Ovechkin scored more goals - I don't really care that he took a lot more shots. He's still shooting far above the NHL average (so I don't think the argument can be made that the team would be better served by having someone else shoot).
Maybe the argument is Ovechkin should shoot less, and pass more? But I don't know if that's true either. In the years where he had 400+ shots, he averaged almost 52 assists. In the years where he had 350-399 shots, he averaged 39 assists. In the years where he had under 350 shots (excluding 2013), he averaged 34 assists. So he actually gets more assists when he shoots more (perhaps because all these shots generate rebounds for his teammates?)
Besides, looking at the yearly shots leaders shows a ton of elite goal-scorers. Bobby Hull led the NHL in shots seven times (his son did so three times). Gretzky did it four times (runner-up to a defenseman a 5th time) Bure, Dionne and Esposito also did this four times. Gordie Howe did it three times (and we only have data for part of his career). Only the best goal-scorers in history are able to take a ton of shots (or else more players would do so).