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.