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.
Maybe "fair" was the wrong word. In the long run, all of those methods will tend to converge on the same payout per hashrate.
However, PPS has the least variance (which is a desirable trait), and CPPSRB is the only known-to-me version of PPS where a 0% fee is possible. 0% fees is its own kind of "fair" in that the pool operator is not profiting unduly -- although of course they should be entitled to cover their costs and to make a fair profit -- my point is that 0% is *inarguably* fair to miners, if perhaps making it harder for the pool operators. Anything over 0% is, at the very least, arguable (although I don't see how anyone could *convincingly* argue that a 1% fee is unfair -- but a 1% fee pure-PPS pool would never survive).
CPPSRB has other "fairness" attributes too. With backpay, you have the potential to earn full PPS for every share you've ever submitted. PPLNS throws away shares after a given time frame; you will never earn anything for them. I suppose that if the "N" in PPLNS is large enough, you get kind of the same thing (since shelved shares that are old enough are unlikely to ever be paid out).