My (albeit limited) understanding of cazimi planets is that it is one way of saving the planet from combustion. Combust planets, whether applying or separating, are unfortunate and so will be severly impaired when performing their duties as house rulers. This is not to say that planets close to the Sun cannot function in modern astrology, and I can also add that the closer Mercury is to the Sun the smarter I've found those natives to be. Within a degree? Genius. But if Mercury combust and not cazimi rules the houses of education...no advanced degree, and your genius could be a fry cook at your favorite seafood restaurant.
According to Hellenistic doctrine the other way a planet was "saved" was if it was in it's own "chariot" meaning in one of the signs it rules by domicile or exatation. Burning is bad, but being in the heart of the Sun was/is the same as being in the lap of the king. If you have a planet that really is within 17' of the Sun...figure out the rest of the story. What housese does that planet rule, what houses does the Sun rule, and everything else. Cazimi is good for the planet, not necessiarily good for the native or the people the native interacts with. An example? My father has Mars (the lesser malefic) cazimi in Pisces in his chart. I don't have a birth time so I can't tell for sure how this affected him re the houses...but I can tell you he ruined many, many lives in his. And that he is completely unconcerned that he did.
waybread points out that cazimi is a traditional idea, and she's right. Because psychological astrology is concerned with how the native perceives things, how the native's mind works, and under what circumstances the native can work with those energies to better themselves. This, at it's core, is not at odds with traditional methods.
This requires an understanding of what happens when planets are setting into the beams, becoming combust, being totally engulfed, and then emerging on the other side. The symbolism is quite beautiful.
The best analogy I can come up with for it (as a mom of three) is just this. A planet sets into the beams (15 or 17 degreess depending on which sources you follow, up to 8 degrees), and there is fear. You know it's going to hurt, and you know there isn't a dang thing you can do about it because no matter what, it has to happen. You can try to run, you can try to hide, but sill, the pain will catch up to you. Planets under the beams perform according to this fear.
Cumbust in an applying aspect (8 or so degrees until you are in the heart--cazimi--), and you are already engulfed with the pain. There is no escaping it because it simply has to be born whether you like it or not, and being in the midst of misery will color everything you do. This is the part where mom starts swearing at dad, the Universe, and her entire condition.
Once you get to the heart (or in my example, the head delivering) there is ecstasy. Literally. The worst is over, and the euphoria is just amazing. It's a moment of complete and pure joy and exaltation.
Combust in a separating aspect is different, because you survived the worst and even though it still hurts, you had your moment and you know that you are escaping the pain. Under the beams in the same separating aspect and yes, you are weakened but again, you know that it is getting better, you are regaining strength and that you are tougher for the experience. You also have hope, not just because you actually survived, but you have something to look forward to (in my analogy, a new baby to love)