Raising the minimums does not solve any problems. It will just take longer for the second arena to reach a level players are happy/okay with.
I think that depends on what the perceived problem is.
Taking the example of at least my understanding of this post, people from outside the " crazy happy time" time zones enjoyed the lack of cap. Examining the reason (it would be helpful to know a more granular reason of why), a "guestimation" would be the lack of caps meant the smaller "total population" of the off hours crew allowed a much higher number to conglomerate together at the same time, allowing for more people to participate with each other at once under the same arena. I'm sure you can agree that there is a gameplay or immersive difference between 100 people in the same arena vs. 200 people in that arena, and the people posting in here appear to prefer the 2nd alternative. By increasing the minimum baseline, it would help alleviate this problem, and no longer split up an already smaller player pool, yet would not alter the "max arena numbers" balancing accomplished by the current cap system when the numbers do become much higher during "happy time". Yes, it would mean the second arena would take longer to reach it's cap, but at the same time would not hinder the "mass online" playability of those players during slower time quite as much.
Was just a thought. =)