I think you’re massively undervaluing shots in general. This isn’t basketball, where you’re likely to get a shot every possession and inefficient shooters hurt you by taking bad shots because you then usually lose possession. Ovechkin shooting more doesn’t necessarily lead to others shooting less.
For instance, when he had 65 goals on 446 shots in 07-08, he averaged 13.5 shots per 60 at ES and 16.1 shots per 60 on the PP. His team averaged 35.6 shots per 60 at ES with him on the ice and 51.8 shots per 60 on the PP with him on the ice. That means, other players were averaging 22.1 shots per 60 with him on the ice at ES and 35.7 shots per 60 with him on the ice on the PP.
Then in 08-09, when he had 56 goals on 528 shots, he averaged 15.5 shots/60 at ES and 25 shots/60 on the PP. But his team increased to 36.5 shots/60 at ES and 66.3 shots/60 on the PP. So other players still shot 21 shots per 60 at ES (a decrease of 1 over the previous season), and 41.3 shots per 60 on the PP (an increase of 5.6). So despite taking an extra 82 shots, the team actually took more shots around him as well. And part of this is because shots can lead to rebounds, or scrambles, they can draw players out of position, and when teams set up, they can often get the puck back and take several shots in a possession