I've had an idea about changing the offside rule for a while now - I can't remember exactly when I first had it, and I may have seen it somewhere else. If this has been proposed before, feel free to post a source so it can get credit.
Essentially, what I am proposing is a dynamic blue-line, very similar to offside in soccer. The offside line would no longer always be the blue-line, but would instead be a line parallel to the blue-line located where the furthest back defender is. The exception is when no defenders are in their own defensive zone - in this case, the offside line is still the blue-line.
The main reasoning for this would be to help increase offensive scoring chances, zone entry creativity, and prevent plays from being called back simply because a player is a fraction of a second off in their timing. Players would no longer have to really worry about straddling the blue-line to stay onside, for instance. It would also give teams much more room to break into the offensive zone. Instead of the defense sitting at the blue-line and either breaking up zone entry attempts or forcing teams offside, defenders would have to decide whether to stand their ground and potentially get blown past or continue backing up and let the offensive team establish control. The powerplay would be especially affected by this. I think the rest of this can be deduced - there are a lot of fine details that could be thought up. Ultimately, I think it would add more strategy to the game and also give more of a reward to creativity and skill.
I also would like to see that offside no longer be a play that can be challenged. Especially with this change, it would be somewhat arbitrary and subjective - two things that should be avoided when it comes to rules and decisions about enforcing them. I would lean toward refs letting the play continue in a close-to-offside scenario, erring on the side of caution.
I can't think of too many drawbacks honestly, other than adding a bit more subjectivity to the on-ice calls the refs have to make. But they already have that with offside as is, and a very similar decision for refs to make was introduced with hybrid icing. I don't think it's too complicated in any way - soccer handles it very well. If there are any pitfalls that I'm simply missing, I'd love to hear about them.