Personally, never shot one. But the idea of a bullet that is on the razors edge of being stable so that, with FMJ ammo, it should destabilize and tumble after striking a target, seems like a VERY limited use case with a LOT of drawbacks.
Regarding the M16 and its ammo, and "designed to tumble" statements are mostly BS.
Yes, the bullet will tumble after impact. EVERY BULLET LONGER THAN IT IS WIDE DOES THAT!
What differs is the degree of yaw, how soon (in terms of distance traveled) it happens, and how noticeable it is.
The .26-.32 caliber bullets used by the world's militaries for most of the major 20th century wars all tumble after impact. Eventually. If they aren't stopped by something before full tumble happens.
Those long, heavy "stable" bullets still tumbled. The difference being it mostly happened AFTER the bullet exited the enemy soldier's bodies, so no one really SAW it happen.
The short, light .224 frequently tumbled while it was going through the enemy. This did cause wounds out of proportion to its small diameter, and this factor was seized upon by advocates of the small round, and this became the myth that it was designed to do that, rather than what it really was, a fortuitous benefit of physics.
The round and its rifling were designed to be accurate. The rapid tumbling after impact was an unexpected military benefit, claimed to have been the idea all along.
Take a look at the history, people were shooting .22 centerfires for some decades before the .223 came along. NEVER any mention of the tumbling and how it enhanced the wounding effect. Why not??
Couple of reasons. First, no one was shooting people (enemy soldiers) with .22 centerfires. Second, what they were shooting were varmint bullets, intended to expand rapidly (even explosively) on targets with very light resistance, compared to the human body or big game animals.
There were some "big game" (deer, primarily) bullets, and no mention of their "tumbling" is found in period literature, either.
The other "myth" one frequently hears about the 5.56mm is that its "horrific wounding power" actually makes it a more effective military round because a wounded soldier takes 2-3 other soldiers "out of the fight" to care for the wounded man.
Sure, that happens, sometimes, WE DO THAT, and so do many nations, who have the resources, and care about individual soldier's health. Doesn't work that way when the enemy doesn't fight the way we do. Nations that treat their troops as cannon fodder, and also those "insurgent" groups without the resources to care for their troops the way we do, generally don't take many, if any guys "out of the fight" to care for their wounded. What frequently happens is the wounded get what care is available, if they are still alive AFTER the fighting is over.