Why is the Eligius payout queue so ridiculously obtuse? Other pools don't have this problem.
It is a feature, not a bug. Eligius is the only pool where the coins will show up in your wallet as "mined" and not transferred in. This means that Eligius never holds the funds in a centralized location that can be hacked (well, not "never", but it tries hard to avoid it). Eligius is what it is. It is the fairest pool around. In order to do that, the creators had to get creative. If you don't like it, mine somewhere else.
If you mean the reward method is fairer than other reward methods then that's not really correct. I'm sure both Luke-jr and wk will both agree that PPS, PPLNS and DGM will all provide fair rewards to miners too.