I don't think the existence of ELO means we should make more use of it - rather, it means we don't need a world championship if the objective is to measure who is best in the win=1 draw=0.5 loss=0 scheme of things (this is, I think, part of Someone's point above). Everyone in the chess world knows Carlsen is the better player, even before we know the results of this match. Likewise, we knew Kasparov and Fischer were the better players. But the matches against Karpov and Spassky were still phenomenal, because they involved psychological and technical depth that couldn't have existed in a mere "tally up the [bigger tournament/overall rating] points" system.
Also, 1-vs-1 gets beyond the ongoing debate about whether draws should count for 0.5 or less, which is nice. More specifically, the question of whether and how to reward being consistent (many draws, few wins and fewer losses) but rarely brilliant versus uneven but generally great isn't as pressing in a match, since it'd (likely) end up not mattering.
That's true. My comment was premised on the assumption that we want to retain a World Champion title. And there is definitely a whole new element that comes into play with matches. If we still want to stick to the tradition of a world championship match, perhaps the best way to do it is to have a double round robin of the top 10 players, and the top two finishers then play a match for the title of World Champion.
Your comment about rewarding consistent but rarely brilliant versus uneven but great bring up another interesting nuance about matches versus tournaments. Fischer complained that once a player gets ahead in a match, there is no motivation to play fighting chess because every half point bring him closer to winning a match, and players are therefore incentivized to play for a draw. In a tournament, that usually isn't the case since the leader will typically have a few players nipping at his heels.
> ... every half point bring him closer to winning a match, and players are therefore incentivized to play for a draw.
This tendency could be discouraged by making wins more weighted realtively than draws: win = 2 points (or, may be 1.5 pts), draw = .5 pts, loss = 0 pts.
Also, 1-vs-1 gets beyond the ongoing debate about whether draws should count for 0.5 or less, which is nice. More specifically, the question of whether and how to reward being consistent (many draws, few wins and fewer losses) but rarely brilliant versus uneven but generally great isn't as pressing in a match, since it'd (likely) end up not mattering.