Thus far, the only actual points I've seen that argues for why an ELO system should exist in PugChamp are as follows:
1) ELO serves as an extrinsic motivator to encourage players to always play to the best of their ability.
2) ELO is used as a performance metric to gauge whether players should be promoted into the *currently unreleased* Pro-League.
For 1), why is ELO the only way to motivate players to want to win? I actually believe many players desire intrinsically to win, regardless of external factors. Many people here are naturally competitive, and that competitive spirit drives players to chase after victory. In contrast, players who simply don't care to try in unfavorable scenarios cannot be made to, even with the presence of an ELO system. I've seen many games where players simply start trolling or even dodging queues just because they've stopped caring on the "losing" side. ELO explicitly deepens the zero-sum scenario, because now there's a cost associated with losing. There are alternatives to encourage players to want to win if their own competitive drive doesn't exist. I actually extensively enjoy casual MM over competitive right now because I only gain ranks for winning, but never lose ranks for losing. I still care enough to want to win, but not enough to just do what Skye mentioned:
Skyesitting on last with a sentry gun and a bunch of offclasses for the last five minutes of a pug.
For 2), in its current state ELO does not in any accurate manner measure the abilities of the players in the PugChamp ecosystem. I know this because I'm 2k ELO and there are plenty of players that are better than me with lower ELO. This is because I almost never get picked in high IM/invite level pugs, so my ELO is relatively unaffected by players who would largely dominate me. Instead, I only play in lower level pugs where I know the odds are relatively in my favor. It doesn't make sense to me that I can farm ELO exclusively without ever getting matched up in a game against players with similar ELO who are actually significantly better than me. In a sense there's two separate ELO pools that are circulated -- one amongst the lower players, and one amongst the invite players. If the two groups never mix, I don't really see how ELO would ever accurately measure which players should play in a "pro-league".
In short, ELO isn't great and several PugChamp admins have already voiced their concerns about it. There aren't strong arguments for why we need it, and plenty of arguments for why it actually hurts more than it help, at least when exposed directly to players.