Well I think the big problem here is you made modern include Untamed which has some of the most overpowered Summoners in the game. Therefore new players aren't interested in levelling CL up because they'll get smashed anyway.
Honestly, changing the term 'Modern' to represent just CL, RW and related Reward cards would see a much more competitive format IMHO.
And I'm 100% sure people would be 'pushing and shoving' to upgrade cards to compete for the higher rewards. But sadly CL summoners are no match for the Untamed ones, so why bother.