In essence: Why would we pick a 9mm, like the Glock PDW or Czech Scorpion, when we can have a 5.56x45? Well...it is a valid question and I will give my perspective on this based on 32 years of experience going into harm's way as well as teaching those who go into harm's way.
Every weapon is a special weapon with a specific application. There are no weapons that handle every possible combat task equally well, and any choice is an exercise in compromise. While we all have personal preferences, the professional, or professionally-minded enthusiast should not have a "favorite weapon". Rather he should be skilled at a variety of weapons so that given some forethought and planning, he can select the best tool for the job.
Now lets recall the concept of the PDW and its pseudo-official definition:
A personal defense weapon (PDW) is a class of compact magazine-fed, self-loading, hybrid between a submachine gun and a carbine. The name describes the type's original role: as a compact but powerful defensive weapon that can be carried by troops behind the front line such as military engineers, drivers, artillery crews or administrative staff. These soldiers may be at risk of encountering the enemy, but rarely enough that a long-barrel weapon would be an unnecessary burden during their normal duties. Because of their light weight and controllability, they have also been used by special forces and by police units.
One point is very important over the others and the decisive point when selecting a weapon to add to the daily-carried handgun.
"These soldiers may be at risk of encountering the enemy, but rarely enough that a long-barrel weapon would be an unnecessary burden during their normal duties."
It will be far easier to go about one's daily urban life with a light and extremely compact PDW than an 5.56 rifle. Again, if the Islmaic Jihad has issued a fatwah on you and has dispatched a bevy of ISIS hitmen to take you out, you would be justified in going about your day in armor, driving a fortified vehicle with a Magpul D-60 equipped M4 at your side.
Those not is such a situation will immediately find such steps impossible to maintain.
Weight. It is not simply about being short and compact as even an HK-91 can be made that way. Weight is a consideration. A heavy weapon is harder to carry, more cumbersome to deploy and slower to use. Thus more likely to be left behind out of convenience. A 9mm PDW is far lighter than any M4 SBR. A Glock PDW is perhaps the most compact of all, specially if equipped with a folding hinge. A compact AR-15 in 9mm, such as the Angstadt UDP-9 (in my opinion, the best of the breed), or a Czech EVO is almost as small as a Glock PDW and far lighter and handier than any 5.56. Thus both are more likely to be on hand and to be deployed.
Convenience. Aside from the weight issue is one of convenience. Having less to bring, less to remember and less to train is a good thing. Being required to stay on top of the manual of arms of a different platform is not a huge problem, but one that needs to be addressed. With the Glock PDW you have the same manual of arms...almost, as your everyday carry handgun. If you have spent a great deal of time on the M4, a 9mm version is an excellent choice. All the better if it takes the same magazines as your EDC Pistol. The magazine issue is not as big a concern and the aacepting of Glock 33 round sticks is not a game changer in my opinion unless you are using a Glock PDW. If you are going bigger, true SMG magazines may be a better choice.
The caliber issue. This is and will remain a controversial point but there are situations where the 9mm is preferable to the 5.56. Unless one has actually fired a non-suppressed 5.56 indoors, with unprotected hearing, he will not think this is a big deal. Will your brain leak out of your ears and all your future earnings devoted to Miracle Ear? No, but the results will not be inconsequential either. And having several suppressors/silencers I am well aware of the possibility of adding one to the rifle, but then you have the issue of weight and length...again.
The 9mm on the other hand does not have either of these concerns in the close quarters realm (the place where these weapons are intended for). An non-suppressed 9mm indoors will not be overlooked, but it is substantially less objectionable than a 5.56. And a suppressed 9mm will allow you to eliminate a crew of home invaders without waking the kids.
The argument about penetration is not as important today with the proliferation of rifle plate armor. In the past one could argue that the 5.56 was a better choice since it would go through body armor like a hot knife through butter. Now, with the availability of armor that is more "rifle proof", that argument doesn't hold as much weight. And yes, such armor is available and prevalent - all we need to do is examine the recent terrorist events in Dallas and other places. In short, if you can buy it, the bad guys can do so as well.
So the answer to defeating impregnable armor is not to continue testing it, but rather to bypass it. We do that with a greater degree of marksmanship skill and greater precision in our weapons. We seek the face shot as a matter of course rather than as an immediate action response. And if we are talking about shooting an adversary in the face, it will not matter if it was a 9mm or a 5.56. Not really. And that being the case, I suspect doing just that with a 9mm will be considerable easier, faster, and even quieter.