Why 10.5-Inches For .300 Blackout

 From "Why I Chose a 10.5” Barrel for My 300 Blackout Build" by Scott Witner:

When chambering supersonic loads, 300 BLK produces more than 1,153 ft-lbs of energy at 10.5″, while 5.56 NATO’s M193 load produces 1,161 ft-lbs in a 16″ barrel.

Also:

... with a 10.5″ barrel, the subsonic round’s dwell time is sufficient to cycle the bolt without the need for an adjustable gas block. At this barrel length, supersonic rounds don’t produce too much felt recoil with a fixed gas block; the gun is neither over- nor under-gassed.

If you’re running both supersonic and subsonic loads, especially suppressed, 10.5″ gives you the gas dwell time to cycle reliably without adding the complexity (and cost) of an adjustable gas block.    

And from "Mike" in the comments:

Here’s the “why” that Scott didn’t cover: in a 125gr super, all the powder is burnt by 9 inches of barrel travel. In 5.56 NATO it’s something like 18 inches. This is a joint result of both the power charge and of the diameter of the flight channel on that caliber. Consumer .223 is usually burnt in 16.

In a 10.5 inch barrel, 300BLK is done burning sauce before the exit, and on Subs, the fire is out about the time she passes the gas port. This is why 10.5 is the optimal full flexibility barrel length on 300BLK      

When I built my .300 Blackout pistol--which was only ever intended for supersonic ammo--I used a 9-inch barrel because that was the point of full powder burn. But I noted that it was just a tad too long to fit inside your standard day pack/book bag. If I were to do it over again, I think I would go with a 7.5-inch barrel for the additional compactness it would offer. 

    As for 7.5-inch, the author relates:

A 7.5″ barrel has traditionally not met the definition of “optimal” for 300 Blackout. The supersonic load loses nearly 20% of its muzzle velocity at that length, while the 190-grain subsonic load loses 10%. Only the heaviest subsonic loads (220-grain) approach nominal velocity at 7.5″, losing around 6.7%.

I think the loss in muzzle velocity would be worth it being more easily stored or packed around in a vehicle.