I'm not sure if you made a good case that random+modifier isn't a good system for distributing loot...[You] seems to imply that the modifier should be greater, not smaller.
That is another option. Essentially, there are three extremes when it comes to loot:
1. Completely random
2. Order determined by a measured variable
Each method has advantages and disadvantages. Option 1 might mean that someone could "slack off" and still win the roll. Option 2 is very sensitive to the variable being measured.
For example, if a tank tanks the end boss all the way down, did she have a greater or lesser contribution than the healer who healed her? Versus the dps? What about AoE on the adds vs single-target DPS on the boss?
I don't know. Questions like that are very hard to answer meaningfully. That's why systems which use Option 2 (DKP, etc.) tend to measure time spent instead.
Completely random makes the assumption that everyone contributes more or less equally, and therefore deserves an equal chance at the loot. This assumption is often false, but a lot of the time it doesn't matter that it is false, because the disparity is "close enough" and it is not really noticeable. The times where the disparity does matter, however, can cause a lot of problems.
So that's the problem with Random + Modifier. The system highlights the disparity in contribution by measuring it (well, measuring something the system thinks is contribution) and telling the players. This moves it towards Option 2: "Player A deserves the loot because he contributed the most" vs "You all contributed equally, so you all get an equal shot at the loot."
Both of those narratives are acceptable.
However, what the WAR Public Quest says is, "Player A deserves the loot because she contributed the most, but we're going to give it to Player B because she's lucky." Or "Player B did a terrible job, but she gets the loot anyways."
And those narratives are very annoying.
Personally, for WAR Public Quests, I think measuring contribution might be more hassle than it is worth. Completely random is "close enough" to be fair (with some minimums to prevent people from afking in the area).