Other than it's well-suited compatibility to a suppressor and short barrel, why not just use an AR10 if one wants a .30cal AR?
Because it's lighter / handier. But good question - the suppressor / SBR role is the main thing.
It's too bad the .338 spectre didn't catch on - the big bro of the .300 blk. Serious penetrating power in an AR15 suppressed setup. Maybe it will yet. The reason is that mags aren't same as 556x45 as with .300 blk.
Is it more deadly / better terminal ballistics on violent human aggressors relative to the 556x45? I think the answer is, it depends on barrel length (but roughly the same). In a 16" + bbl, I'd rather have a 556x45, or almost equal. But in a 10 or 12" SBR, where you may lose the yawing/disintegrating effects, I'd take the full-power .300 blk over 556x45 any day.
So that's the dual-role key to the popularity: In one rifle, if you SBR and suppress it, in a VERY light handy rifle, you have two roles in one: Silent fighter, and regular fighter roughly equal in terminal ballistics to 556x45 *for that same barrel length* anyhow (and possibly better in the intermediate barrier penetration department).
If you don't SBR and suppress it, the .300 Blk makes little to no sense. Particularly if it's not even SBR'ed at least. So, if willing to do NFA stuff, .300 blk or 9x19 make nice handy carbines. M4gery or longer, 556x45 or other chambering is the way to go (6.8, 6.5, etc.). If you want a 16" or longer .30 cal AR15, the .30 RAR has more oomph. But then again, why would you want that, when the 6.8 spc and 6.5 grendel are superior to any .30 cal AR15 for most purposes, in a 16"+ bbl?
Oh, and add a Slide-Fire doodad if that's your thang, and you've got one neat rifle - how's about a full-auto, suppressed, super-handy SBR with a 200 gr .30 cal bullet that's still pretty flat to a good 125 yards? Not too shabby if you can afford to shoot such. Only thing better would be same in .338 spectre with 300 gr .338 Sierra SMKs!
Oh, but as others have mentioned, that's the theory - but back to reality - if you don't handload, good luck finding ammo!