It's important to remember that the Browning Automatic Rifle may have been deployed like a machine gun, but it was not a machine gun. Instead, the rifle was envisioned to be utilized in a 'walking fire' role, where by a single soldier may require a machine gun like volume of fire, in specific situations, during an assault. Although the rifle was light- a Colt variant of the rifle called the Colt Monitor Machine Rifle is the lightest fully automatic firearm chambered in 30.06- it was also very heavy. Excluding the Colt variant, which was still 13 pounds, the BAR weighed anything from 16 to 24 pounds. It's characteristics meant that between being a traditional target rifle, a volume fire weapon, and a machine gun there was always some feature that disagreed with it. The BAR was very accurate, but it was twice as heavy as the M1903 Springfield which fired the same round, and kept most of the magazine capacity. The BAR could be used in automatic fire (and indeed the fire select was 'automatic' and 'automaticer') but in terms of it's ability to hold physical geography even if it were about 1/5th the weight of an M1917 machine gun (full munition belts, tripod, gun, and water) it lacked the staying power and sheer capacity (the 1917 firing 250 round belts). Even as an infantry operated rifle it was still about 6 pounds heavier than the new kid on the block in WW2, the M1 Garand. Which also fired 30.06.

And if your brain is doing that thing.... yes. Every standard issue rifle the US was fielding at the onset of WW2- excluding the M1 Carbine which fired the .30 Carbine- fired Springfield 30.06. And the M1917 machine gun. And the M1919 machine gun (for the US at least). The US really liked it's full rifle cartridge and in terms of the cradle-to-grave life cycle of introducing a completely new weapon platform, not having to worry about it's munitions is a ton of work taken off the shoulders of logistics.

I'm not going to get into every precise situation- although for the Japanese the lack of industry was probably a deceptively important factor; the Type 11 wasn't even strictly a domestic design, having been based heavily off a French machine gun while the type 96 was less 'heavily based' and more 'heavily inspired' by a Czech design- but the problem with this question is that it presupposes that everyone had a firm idea on what an LMG needed to have.

And then the Germans asked a company- Metall und Lackierwarenfabrik Johannes Großfuß AG- who for it's entire history had been making stamped metal lanterns, "Hey, can you make a machine gun for us? These MG34's are great but they're also ruinously expensive to make." So the company, absent any experience making machine guns, dispatched one of it's lead design engineers to attend a training camp for machine gun crews, and had him ask soldiers some questions on the weapon platform. Then he took an existing Mauser design, and ended up the the MG42. And while the MG42 did have glaring design issues- the machine gun was so adept at chewing through ammo that the entire infantry unit could be drafted into belt-carrying duty, the machine gun was so adept at chewing through ammo that it could eat itself alive through simple misfires, the machine gun was so adept at chewing through ammo that replacing barrels was a fact of life, and a design concern which meant it couldn't replace the MG34, etc- it was superb as an infantry operated machine gun. Roughly half as expensive in every sense of the term- less expensive, fewer precious materials, less time relative to the '34- and for performance almost identical to a standard machine gun, it only weighed 25, 26 pounds and was conceivably operable by a single soldier.

This sorta came out of nowhere for machine gun designs. Previous machine gun designs assumed limited transport (a 100 pound machine gun kit is going to get split up between personnel) or accepted certain concessions to take a machine gun like performance or design and place it in an infantry-operable design. The MG42 made heavy use of light, cost saving stamped metal parts where Americans were still obsessed with machining everything (machined parts are both labor intensive, requiring highly skilled personnel, and take time to make relative to something made by a machine that punches it out of sheets of metal.) All that weight saving meant that while the MG42 did carry certain expectations (every set of boots on the ground could be drafted into the logistics detail ferrying belts of ammo for the thing, changing barrels was a fact of life which meant it was not suitable for use within the hull of a vehicle, etc) it also meant it wasn't a 'diluted' machine gun experience; the MG42 was a viable LMG, it was still perfectly capable at performing as a traditional machine gun.