I agree, a 5.56 or 7.62 carbine is better for HD, no doubt.
For me there are lots of little reasons (many particular to my own circumstances) that make it worth it to me, but no single overall compelling reason. Here are a few:
Cost of cast lead 9mm reloads and ease of straight wall vs bottleneck reloading
Local range will not let you shoot rifle rounds at less than 50
Related to above, can actually see my holes without spotting scope
Similar recoil to 5.56 but less blast which makes it more enjoyable for me and new shooters
Easier on steel targets
For whatever reason, I love the feel of a 32rd stick mag
Doesn't heat up much under rapid fire
Anyway, those are a few of the reasons for me specific to training with a 9mm AR. Many are personal and circumstantial, but like I said, it is one of my favorites. I like it even better than my 6720, but if I could only have one, it would be the 5.56 6720.