I love the current system but... What I would like to see is some building-onto the current things. I kinda agree it could perhaps be open AFTER the E4, that way it is essentially "optional" content and the younger audience who may not be able to grasp the concept/figure it out, are not forced to try and figure it out to progress.
Also... I kind of see a huge flaw with the E4. Essentially, as the E4 champion, shouldn't YOU get challengers? I think it'd be nice to receive challenges (perhaps you are called when there is a challenger, or etc?), it'd keep the game a little ever-changing and give it a little realistic charm. Perhaps not the best idea, but I still find myself a little puzzled about it. It would add some more battle opportunities, and isn't that always a good thing? :)
It'd be nice if perhaps they made the plots longer, and even gave you options of what to do in the plot. Would perhaps make it less linear? (-is still sad I couldn't join Team Rocket in RBY- Nugget Bridge was a lie! :( )
As for gyms, however, I think they honestly should be stronger. I mean, seriously... First gym ranges from 10~20. HOW on EARTH did that gym leader get ALLOWED to have a gym? Now, I don't mean make them level 100, but a little added difficulty couldn't hurt. :) I don't think they're holding Pokemon back, but they do leave a little to be desired.