You guys just keep upping the ante.  First the claim was that an MC shouldn't try to control the rate of advancement, which I found hard to agree with, but is nonetheless a reasonable opinion to hold.  But this is a design thread, in a forum about making hacks.  Are you saying that the designer, too, should not deign to interfere with the mysterious powers of the game?

Somebody (well, vincent) made up the rule we have now and presumably had reasons for doing so.  *I* like to think that Vincent had an idea in his head of about how many improvements per session to expect and that if the rule didn't achive that result he would have changed it. 

I must be misunderstanding something because you seem to be advocating a contradiction in terms, that a game designer should not try to control the experience that his game generates.  But that's what game design *is*.  Culling, from the literally infinite number of play experiences it is possible to have, characters it is possible to imagine, and stories which it is possible to tell, a subset which the designer endorses as especially enjoyable. 

Semi-longtime lurker, first time poster, but anyways...

One thing going on here is, Orion, is that you said you hadn't finished a game of Apocalypse World run under default rules. Which makes it more likely people are going to go 'of course he doesn't get it because he hasn't tried it', and advise you to try it because they like how it turned out. Or because they think even if it doesn't turn out how you want it to, that will give you a better idea of why it doesn't work.

But I think the main issue here is that your stated question is 'What is advancement for?'.

With such a question, people are going to reply with what it is in their view of default Apocalypse World, since there is no explicit talk of hacking, even if it's in the right forum. It seems like you're asking how the game works, rather than how it could be changed, so that's what you're likely to get.

People sometimes ask such questions to understand the thoughts behind the design, which can be useful for hacking.

If you named a topic 'How do I change the rules to control advancement as MC?' or something, people are more likely to be helpful, as you're then clearly asking their advice on how to change things, rather than how advancement works by default, or if it's a good idea.