First of all I want to express that CF is multi-dimensional game and here I'm only talking about PK competition part. I don't touch player interaction, RP "competition" and other aspects of the game that are also good reasons the play the game.

Are there advantages and disadvantages between different players? Sure. But those advantages are not necessarily equated with who is an immortal or who is not.

True.
For example, I consider myself above average when it comes to CF knowledge ( though certainly not the best ) and it gives me some advantage. But I'm ready to give away that advantage by opening related information. Because I feel sorry for newer players. Hehe.
Also I prefer to see competition in how you apply public information, not the amount of info you possess.

Fundamentally speaking, most imms are good players not because they are imms, but because they are veteran players.

False :)
They are good players because they are veterans AND immortals.
After all, there are many veterans who weren't immoratls and they are overall less good.

Being an immortal gives you great advantages in PK.
The snoop comand alone may greatly increase your PK skill.
If you watch skilled people in action, you study their behaviour patterns, their hidding place, wand locations, etc, you become much better in PK.
Code knowledge gives you another edge. If you know important factors in assassinate success, if you know what is improtant for bashing you may capitalize these factors and become more dangerous in PK.
Areas knowledge is another important factor where immortals have advantage. For example, if I don't know what amulet of Ultimate Evil does, I may just drop and sac it because it may look as it does nothing. And I didn't know that pre-Cabdru.

You really don't want equity. At least *I* don't want equity.

There will be no equity if game mechanics are public.
There is some distance between knowing something and properly using it. That is where player's experience, overall skill, smartness, luck comes into play.
For example, you may describe how exactly flurry works, what are significant factors in its success but you would still have to learn when to flurry and when don't. That would make "fair" competition between immortals and mortals.

Your analogy to games like chess or football are irrelevant because games like chess and football DO have inequities. Some players are stronger, faster, smarter, whatever.

Some players may be smarter and thus win. But they win because they are smarter, not because they create the game and don't tell others how it works. When a stronger boxer wins a match, people usually don't blame him for being stronger and he doesn't really want to stay anonymous to avoid blames. But if you create a game and win because you know something special that other don't, well, you should be ready to be blamed.

Instead, the factors of competition in CF are in part items and knowledge. It's what gives the game longevity, to constantly be expanding your knowledge and thus improving your game.

Here is a dangerous place.
A while back I would agree that striving to expand your knowledge and improving this way may add longivity to the game. But when it comes too far it becomes the game's grave. Newer players start far behind and have no real chances to compete with veterans unless they put a few years in. Some of them actually just give up. And as I said before I know several old players who stopped and don't wish to start again just because they are "afraid" to be far behind in knowledge.

If everyone could just look up locations of items on a database somewhere, it would remove a factor of long-term competition.

No, there still be a competition in proper using them.
Everybody knows chess rules, a few are good at applying them.

Not to mention, it would ruin the exploration element (which is fun for a LOT of player-types, myself included). Even people who refused to look on the database are screwed out of exploration challenges when those things become common knowledge.

I'm irked each time I hear that argument.
There is a fine border between:
1) loving exploration
2) loving advantages that exploration gives above those who didn't explore this or that certain place.

If you like exploration you are not obligated to look into databases. Go ahead and explore. You will have fun.
If you like to have an advantage because you explored something that Joe Blow didn't, well, after sharing info you may lose that advantage. Is that really bad for the game?

To take an extreme, everything would be *most* equitible if you just dropped everyone into the game with identical stats and sub-issue items, popped them all to level 51 and queued them into equally balanced fights in some perfectly balanced battlefield.

That's how Quake or Chess works :)
Still they are great games with a lot opportunities for competition.

You may leave CF as it is. It still be a good game.
( Like "Heroes of Might and Magic 5" without a good manual, where you have to figure everything from your own experience. )
But I've noticed that a such games are appealing for younger people ( 16-years old ), but, in general, elder people, once they gain some experience in games and life, come to conclusion that, public game-mechanics usually helps to create more solid and long-living games.
And when you keep secrecy as a key basis of the game, implementors will always have big advantage and you are not going to solve ####storm problems when immortals play the game and actually use their advantage. Anonymity is avoiding the problem, not solving it. ( Keep in mind they aren't obligated to use their advantages. For example, Nepenthe may create a herald ranger and just drink whole time in the Inn, nobody would cry about it ).