Checks get finished because the risk is low and the reward is high. You can potentially knock an opponent out of a game/series by “finishing a check” and there is very little risk of incurring a penalty given the way interference is enforced.
HTFN's done a good job illustrating these hits from the perspective of the checker, but a rule change would also change the perspective of the checkee.
In a world where you're effectively giving someone more time to make a decision, they're just going to use that time in most cases. So that part wouldn't change much, if at all. And what's left would just be making a key part of the game taboo.
I think the current thresholds are fine. If they want to adjust what's allowed in finishing a check so that you can't full-on kill a guy away from the puck, great. But understand that'd be one of those "I know it when I see it" types of rules that everyone hates and will be haphazardly enforced, causing everyone to hate it even more. It's already pretty much that way now.
At some point everyone involved needs to accept that there's inherent risks in being a full-contact professional athlete. Sometimes firefighters get burned, cops get shot, pilots crash, divers drown, and assholes get kicked in the sack. There's occasionally a real cost to doing what you love.
Wear a fancier helmet. Learn to duck or move or make that decision faster or take that hit better. No one wants to watch Nerf Hockey.