The rewards of exposure aren't all that rewarding
I guess the primary "obvious rewards" would be book deals, television appearances and the like (unless I'm missing something more "obvious"), but to really capitalise on those you'd probably need to commit a lot of time to it (likely giving up your day job, which may even pay more), there isn't much of a guarantee that people will care much or believe you and people will lose interest soon enough (so it's only temporary profit). You also need to want that fame (or need the money), which could potentially be detected and avoided in any new members that are recruited to a reasonable degree.
If you try to go the route of exposing their crimes to the government, the most you can probably hope for is not being charged yourself. Unless you want to opt for blackmail, but that's a whole other can of worms.
Not to mention anything you yourself did for the organisation may affect your future career outside the organisation and/or your freedom.
Then there's the question of how much information you actually have to expose. The top-level members will probably have some huge secrets, but what the low-level members know is probably a lot more limited, not that extreme and less believable if they're not a prominent figure in society (which would probably typically be the high-level members instead).
Even if you just contrast this against the direct benefit of being a member, exposing them already doesn't make too much sense. Then add all the reasons mentioned in the other answers and it really doesn't make sense.
The most compelling reward is likely morality and wanting people to know about it, but the organisation has already failed if you recruit people motivated strongly by this.