Not quite, Chit. The real answer why hollow point ammunition is not used is because it sucks ass at piercing armor relative to full metal jacket rounds. Full metal jacket rounds are tougher allowing them to maintain a point upon impact and thus more easily penetrate armor. Further, the standard 5.56 rounds were designed to tumble so as to create more tissue damage, likely just as much as hollow point rounds without compromising its ability against armor.
Armor hasn't been encountered very much in modern conflicts, though. In a fight between large, organized militaries, sure. But by and large, the insurgents, guerrillas, and rebels that modern armies have been fighting have had little to no body armor except what they can steal or purchase on the black market.
And while 5.56x45mm rounds were designed to tumble, they often don't. It's still a point of contention as to whether the heavy bullet and new rifling twist in the M16A2 and A4 have made it less likely to tumble on impact, but it's less contentious that a shorter barrel length results in a lower chance of tumbling at longer ranges; the M4 tends to have more problems with wounding than the M16, and the US military is trying to make a massive switch to M4 usage among general infantry due to the convenience of the shorter gun and adjustable stock.
The problem is that such a small bullet relies on tumbling or expanding to create a suitably large wound channel to cause organ failure, rip blood vessels with glancing hits, and disrupt tissue and cause shock. If that bullet doesn't expand or tumble, you have a 0.22 inch hole. As important as penetration is, so is the size of the round to compensate for discrepancies in accuracy.
