I think the District's point system is pretty good, but of course there needs to be some way so that those teams that can only afford one regional, but do very well can be compared to those that do well in multiple events.
That being said, the teams that enter Championships currently do deserve it. EI award winning teams are great inspirations on how to run and function as a team. There's the argument that the third alliance partner shouldn't move on, but that third alliance partner can be, and is often, essential to the victory. I'm pretty sure everyone here saw the Finals Matches for the famous GTR-west regional this past weekend. If you haven't seen it, here's a link:
http://www.ustream.tv/recorded/21501483
2200 and 4001 didn't seem like stellar bots, but they really did make it possible for the Blue Alliance to win the regional. Their defense and their place in the strategy made it possible, and their unique and key role in the winning strategy deserves a spot in CMP.
That being said, there are teams like 118 that deserve a spot in CMP as well. Look at their OPR. It's a solid 33.9, ranked 6th in all of FRC. This is higher than 1986, 148, and 16, who've all won 2 regionals already. 118 has been amazing, and had bad luck as the only thing preventing them from moving on. If anyone watched the CT regional, 118 had comm issues in their semis, which was arguably the only thing preventing them from moving on.