If you take in consideration the level of performance and typical expectation of a 9mm pistol cartridge to be effective and accurate in the hands of a competent user at 25yards. Then you can expect a typical 9mm round based on that same envelope being shot from a rifle with iron sights and to gain 50 yards. This translates to a 3x increase in overall effectiveness. Not too bad if you look at it this way.
A typical auto pistol with an 4 inch barrel has a sight radius of about 5 3/4ths inches and a 16 in barreled rifle at 12-13 inch if it has a barrel mounted rear sight and approximately 24 inches with a rear sight located on a tang or rear of the reciever. These are all guesses as this well vary rifle to rifle. It is a generalization for illustration purposes. YMMV. It is still an increase of 2-4x in the sight radius on an iron sighted firearm, which is going to give you about that much more in accuracy. Although it may not mean you will be able to shrink your groups accordingly as that will be realated to the ammuntion and mechanical accuracy of the particular rifle in question, along with your ability to utilize it to the maximum as well.
What you will gain in extra barrel length, increased sight radius, more stable sight picture from having a stock and proper cheek weld makes it a worthwhile consideration for applications where the intended target is the same as it would normally be.
In the case of the 9mm. We are in general looking at two legged predators. It is reasonable to expect 75-100 yards out of a 9mm carbine and the potential of being twice as accurate or faster shot to shot is somethng to consider. Imagine the confidence increase to know that shooting a 4 inch group at 25 yards is a cake walk compared to shooting that with a handgun.
It won't match what a .357 Magnum would gain, yet at the same time, you can't be sure that a 300-400 fps increase in velocity out of that round using a bullet designed for SD won't fragment prematurely and fail to penetrate deep enough. Granted you can use a more heavily built bullet in a .357 Magnum chambered rifle and gain a great deal more then any 9mm could ever hope to match, it would still be related more to you intended use of said chambering and loading.
A 9mm carbine or similar would be significant improvment over a pistol for self defense, especially if you are not the best shot with a pistol. Wether it is from lack of money to train, lack of time or just plain old laziness. You can be better served , yet there are drawbacks as well. The increased size of the platform will make it far easier for you to be disarmed and it may require both hands to be effective with, whereas a pistol can be used with only one hand and the shooter should be able to be effective with only one hand using a pistol.
Yes the two handed method, with a pistol, is more stable and lends itself to faster follow up shots and to some degree accuracy, but it is still a handgun and the original intent is one handed operation, with the second hand being considered a luxury you may not always have in certain situations.
I say a carbine or rifle chambered in 9mm my not be the best compromise. Much like the idea of coyboys using the same pistol round in their levergun it holds up in the modern age to the same scrutiny. It is a compromise and within those limits it may well prove to be quite useful.
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Dr. Dirt Nap prescribes two nuclear nytol, up the potency of the dosage, and they call no one in the morning. May they sleep well.