Although a lot of people complain about the ridiculousness of it being called the "Champions League" when usually most teams in it are not even champions, that won't change now as it has such a strong brand identity. I would like to see more genuine country champions included but if you try to cut back on the big league non-champions then any proposal will be thrown out as they need their snouts in the trough.
Therefore, a compromise to me would be to double the participants to 16 groups of 4 (64 total instead of the current 32). The last year's UCL 4 semi-finalists and the Europa League finalists would automatically qualify, along with the champions from the top 36 ranked countries (4+2+36 = 40).
The other league champions can be in a one round play-off with the rest of the 2nd, 3rd and even 4th placed teams - this gives an additional 48 teams a chance to qualify (40+48 = 88, so it opens it up to slightly more teams than currently have a chance - think it is about 80 at the moment).
I know this probably won't happen as average TV ratings will be down in the short-term, but not as much as moving them from terrestrial telly to satellite telly.
Also, the big league runners-up and non-champions would have to start their season a fortnight earlier and so they'd miss out on these stupid high-paying lucrative pre-season rip-off friendlies where they earn £millions for glorified training matches (BTW - this another stream of revenue currently being denied to teams like Celtic at the moment due to us/them being so focused on European qualifiers).
I can dream, I suppose!