My reasons for having my 870 as my primary HD long gun are these:
I have my HD G20 with X300 light in the quick access lock box for initial bump in the night and then assessing as to whether I need to take more time to access my long gun(s).
My wife grew up around Pump action shotguns and is reasonably comfortable with working them. I keep it chamber empty and safety off so that she only has to work the slide and she's off to the races. It's LOP is shortened so that she can make it work pretty easily. She is not familiar with ARs and is not really interested in taking the time to retrain.
As has been mentioned in this thread a few times, 5-7 rounds of 5.56 is not a bad idea to plan on needing per threat. When you talk about that kind of ratio, a 30 mag gets used up fairly quickly. Starts to put the 12 gauge being closer to as being able to serve as many threats as generally fewer rounds are needed with solid hits. Yes, I know, there are always exceptions to any generality, but 12 gauge usually does a pretty good job.
I'd also rather have my 870 involved in an investigation and the subsequent loss of said firearm until it's return, than my M4. If I was to have to use my 870 in an initial event, who's to say someone might take issue with me and seek out revenge and then I think having my M4 available would be advantageous.
I like being able to go from limited penetration #4 buck first round, then 00 for most of the remainder (mag tube + side saddle), then a couple rounds of slugs. This gives me quite a few options depending on the situation.
I need to get me a patrol bandolier like what Eagle used to make IIRC. It had loops for 12ish rounds and a couple pistol mags. Nice to stage along with the noise dampening electronic ear pro.