Allure? That's subjective, much like trying to explain why one girl appeals to you more than another.
In the day, I didn't much like the idea of M16's at all. Initially they were new and cool, but that quickly soured listening to old school .30 cal advocates who were themselves relics from previous wars.
Tactics and hardware change to meet new challenges.
I grew to understand what the M16 was all about because I had to use one, even tho my personal rifles were "superior." I used them literally from one day to the next for 22 years in the Reserves, shooting the M16 one day, and getting off early enough to deer hunt late Sundays with .30 calibers.
To start with, self loading rifles are superior in shooting. You don't disturb the sight picture or move your hand from the trigger, you simply acquire another target and squeeze again. Bolts and levers don't let you get quick shots. They are inferior in the overall scheme of shooting. Magazine fed rifles have more ammo, again, reducing the down time otherwise better spent shooting. Large capacity mags do a better job keeping the shooter busy putting bullets downrange with fewer interruptions.
The AR15 takes it up from there by having less parts and simpler engineering that is more elegant, both of which contribute to being superior to manual action or piston guns. Extra parts mean more parts to break or malfunction, all of which contribute to not shooting. The AR dispenses with not only parts that aren't needed, but also reduces the number of stressed parts to the minimum, and has created a new standard in firearms construction in the process. The aluminum upper and lower receiver only hold the parts together, and have sufficient strength to be used as a lifting device capable of hoisting a soldier with full kit into a window. But - it doesn't have to withstand any of the forces of the powder charge whatsoever - that's exclusively handled by the bolt lugs and barrel extension screwed to the barrel. The receivers are never stressed with it, unlike almost all the other guns I've used.
Screwing the barrel extension to the barrel means no press, heavy equipment, or expensive labor is needed to perform the one task that is critical - setting the headspace. It's a micrometer like screw adjustment, and takes just a few minutes on a work bench. It's also so consistent and accurate that the AR 15 can be put together from parts made 1000 miles apart and it safely shoots. But- headspaced with it's own bolt, it increases accuracy more easily than the difficult and harder to perform methods of pressing a barrel into a receiver.
That receiver is a closed top with integral scope mount, and one accepted in a universally used system that can clamp iron sights, red dot optics, or even scopes costing more than the rifle itself. Eye relief can be set for it's most optimum distance, not a forced situation where the shooter has to conform to the rifle. That's called being ergonomic - having the tool fit the user, not forcing the user to fit the tool.
Another set of features are the controls - safety, mag release, and bolt stop, that operate the weapon along with the trigger. The AR doesn't force the shooter to remove the trigger finger to shoot - it flicks off with the thumb. If he empties the magazine, he then uses the trigger finger to drop the magazine while the off hand inserts the new mag and then drops the bolt to chamber another round. All this can take place in just a few seconds, all while the shooter continues to keep the sights on the target ready. You don't have move the trigger hand from the grip, lose the sight picture from being forced to move your face away from operating parts, or have the target simply walk out of sight.
Frankly, very few of us prefer to operate primitive cars on a daily basis, the majority sold these days have automatic transmission, power steering, power brakes, even air conditioning. But - often enough, the Iphone using owners revere old antique firearms designs as if they are the epitome of the art. In fact, they are not, and never will be again. Modern firearms are simply better, more accurate, and easier to use. It's not about allure at all, it's about using a better tool, rather than deliberately choosing inefficiency or even clearly proven deficient engineering.
Nothing immoral about them, but a bolt action rifle is no better than a dial phone on a 30 foot cord. It has it's limitations, it can't hold a directory or even allow one touch dialing. Nobody much reveres that, and AR shooters don't necessarily prefer slow firing, heavy, inaccurate guns that impede what a shooter should be doing - finding a target and pulling the trigger. The AR is clearly superior to manual action guns, and that's the point - not "allure," or some other psychosexual distraction.
That superiority is exactly why most new designs for a soldier's rifle blatantly copy features that are part and parcel of the AR15 - because they are clearly better. The rifle simply helps the shooter to shoot often and well, and designs that incorporate those features are what are being adopted more often than not. It's basically a matter of window dressing the weapon so that it doesn't resemble the AR, all to get it accepted because it does emulate the AR.
The difficulty isn't with the guns, it'w with those who lack the understanding to see it, or refuse to because denial is more comfortable than admitting the truth.
Especially when you have it already bought and paid for at probably a fraction of the current price. But if you ask for opinions on the internet, be ready to get them!