NHL GM's most certainly will care, because they might well be fired before Michkov comes over to help what is no longer their team. Teams that draft high up are teams that are performing poorly, and are under great pressure to get better. They can't afford to wait 4 years for #1 or #2 oa player to show up, in the vast majority of cases.
This has nothing to do with Michkov's ability, or his attitude toward the situation.
I mean, if the 2023 draft were the 2021 draft then Yzerman MIGHT have enough goodwill with fans and management that he would pick Michkov over some none Bedard top prospect, but they have been losing for a long time, as have Buffalo, and Ottawa, etc., etc.. Asking a team and their fans to wait all those years for help to come is a BIG ask. This is not like the Kaprizov situation, who was an afterthought during the 2015 draft.