Deeper analysis on the topic... (I affirm the truth in your post and just wanted to clarify some things, I do believe with Sliq's reasoning that these matches would take far too long, therefore items should be banned)
What you were talking about is formerly known as (in statistics) as the Law of Small Numbers or the Poisson Distribution (
http://en.wikipedia.org/wiki/Poisson_distribution). Basically, what I want to derive from that is that there is a possibility of variation from the expected results.
Try this little activity. Get a coin, any coin that has around 50/50 chance of getting heads/tails. If you are paranoid of a US coin being weighted on the heads side and under weighted on the tails side then feel free to take out your Graphing/statistics/etc calculator and do this. Write down H or T in any order in any frequency 10 times, but do it so it seems random. For example: H H T H T T T H T H. Observe your data and check to see if you have a streak of 3 heads/tails. If you do NOT then you are considered an outlier as the "chance" of having a streak of 3 heads/tails is ~80%. Go ahead and try it with your coin.
Basically what is being established is that chance is not reliable if there are only a few values. A possible rebuttal is that there are a vast number of items (Mr. Saturn and co) that are not as advantageous as say a Ba-Bomb. The reality of the matter is that it would not be until a really long time until the chances are averaged out. This is where the Law of Large Numbers comes into play (
http://en.wikipedia.org/wiki/Law_of_large_numbers). Go to that wiki link and check out that picture. Notice that not until ~350 rolls did the Dice roll
somewhat align to the average roll of "3.5". This basically means that not until you play with an absurd amount of lives (at least 50 I would say), would you be able to declare it as "fair".
Now let me put this into perspective. Let's take... Azen vs "Not-So-Great". Clearly, Azen should win his games. Now if they played only with one life, the chance of "Not-So-Great" winning is anywhere near as low as with 99 lives. In fact out of 99 lives, Scrub would loose for sure. So let's say "Not-So-Great" gets Azen for the first stock of 4 with the aid of a ba-bomb. The chance of him getting another great item is in fact not low.
Naturally the chances of getting a kill item would be different depending on how many items there are in the first place. But the point still remains, not until a vast number of games (even 100 may not be enough) you cannot ascertain the true victor.
This argument may be able to be reversed in perse Azen vs ChuDat matches. Both players are good and perhaps ChuDat could have won Smashacatalysm (or however you spell it) if they had played 1000 matches. But that is simply not practical. The truth of the matter is, is that with fewer variables (maps elements, items, mindgames, etc) the sooner the average will be reached. Therefore, tournaments try to eliminate all sort of randomness that could possibly explode in to one player's favor while at the same time maintaining the fruits of being good at the game.
I mean, think about it. If soccer players were randomly given stuff while playing, such as lets say... Chuck Norris can RANDOMLY com from the stage and roundhouse kick the ball into the goal... fictional but gets my point across, it would be madness. (this is not fun by the way)
OK I said all this but I didn't bother reading all the pages of this, only the first 2 and last 3.
Well there's my input for you and my first post as well.... (lurkmoar?)