If you’re more of a Johnny-come-lately than a summa cum laude (watch that snag in all the spam filters), if in fact you’re perhaps a bit non compos mentis, you might well be a nincompoop. You could be a rich nincompoop – there’s nothing requiring an income pooped out – but if you remain a ninny, a cumbersome old poop, then you get the one-two-three punch of this word: nin – first at the front, on the tip of the tongue, with a high front vowel sliding into a nasal – com – a bounce from the back back to the front by way of a central vowel, rhyming with dumb – poop – a little puff from the lips, like blowing off a bit of fluff, but the vowel is high and back, so the sequence of vowels is front-mid-back while the consonants start on the tip of the tongue, bounce off the back and end on the lips.
It makes for a good effect. I recall a Bugs Bunny cartoon wherein Bugs is deriding a nemesis only to be bonked on the head and left in a daze: “Why, you big nincom… [bonk] …poop!” with the “poop” on a high note. It also has a modest flexibility, as when Frank Burns in M*A*S*H referred to a non-commissioned officer (corporal or sergeant) as a “non-com-poop”. And the repeated letters – n and n, p and p, and those googly eyes oo – add to the childishness, as repetition often tends to do.
No doubt the excremental undertones of the ending of the word help maintain its dismissively derisive tone. Not that the poop is necessarily the fecal one; it may be from a less common word, a verb meaning “cheat”. But that word in its turn likely has influence from the dung, perhaps through the back door, as it were. And from dung to dung returns – the word poop in you old poop (as in Katharine Hepburn in On Golden Pond) is likely shortened from nincompoop.
But whence comes this word entire? Samuel Johnson thought it came from non compos mentis, but there is no good evidence of this, and the oldest forms (mid-1600s) appear to be nicompoop – the second /n/ coming later. A later writer, John Ciardi, followed the sound-coincidence trail of folk etymologists everywhere and decided that since there was a Dutch phrase that could be constructed that sound somewhat similar and meant something kind of similar – nicht om poep, “niece of a fool” – it must be the origin, even though there was a lack of any other evidence to the cause (such as actual instances of usage of the Dutch phrase).
In truth, the best evidence is that it’s formed from Nicodemus, via French nicodème meaning “simpleton” or “naïve person”, with the derisive poop tacked onto the end in place of the original final, and extra nasals inserted along the way. That’s not certain, but it has more to back it up than the other proposals. But evidence doesn’t always manage to get in the way of a cute story, a contrived sound coincidence, or a dedicated nincompoop.