Why was the US and not Britain or German mass manufacturing the .50 cal? Particularly the M2 heavy machine gun.
I recently touched upon this subject here with some excellent input from /u/the_howling_cow and /u/buy_a_pork_bun.
Howling Cow's follow up in particular is a telling first-hand account of the .50s effectiveness.
In addition, from my posts:
Its the mid 1930s, a 37mm cannon in a tank is considered on the higher scale of high velocity weaponry still. The .50 BMG can still defeat most armored vehicles at combat ranges at this time, was cheaper, smaller and easier to train with than a 20mm. Unsurprisingly in this context the Americans were keen to keep it hidden.
The usefulness of the .50 Cal for recon by fire, 'painting' targets for other vehicles, emergency anti-air defence and general suppression fire however, was rated highly by all who saw it. Its flexible, multi-purpose caliber kept it in service as a commander's mount or AA mount across all vehicles.
Although the .50 cal's ability to be an armor-defeating weapon was basically dashed immediately, it remained a cheap, light, effective alternative to the 20mm. Furthermore it was almost in universal service across the US armed forces by the year 1940 - so not only do they have a reliable, robust multi-platform weapon, but they have it standardized. In addition to all its power as a large-caliber weapon, it had the added benefit of being sustainable from a logistical standpoint.
Doctrinal differences and priority defined why the British and Germans rather used 7.7 and 20mm equivalents in their aircraft and ground weaponry. Like the US, in an effort to standardize it was unsurprising that their AA mounts often were 7.7s and 20mms as well. Its good to remember that the .50 caliber is a pre-war weapon for the US, its already around in great numbers, and the US's run-up to a war footing was done at breakneck speed. In many cases, they had to use what they had a lot of/was easy to produce, not what they truly wanted. They just happened to hit the jackpot with the .50 cal in terms of usefulness. In short; nations all had their own domestic industries.
The .50 cal could and often would be employed as a crew-served weapon, it could be tripod mounted by as little as 3-5 men if necessary. While the other nations often had crew-served, relatively mobile weapons such as 20mms and even 37mms, they were large, high silhouetted and could carry little ammo organically in comparison to the .50 cal - in which every man in a crew could carry a belt of ammunition without too greatly exerting themselves further.
The British had their own version in the .50 (12,7mm) Vickers, which fired 12,7x81 ammunition, while France (and a multitude of other countries, including Sweden, Belgium and Romania) had the 13,2mm Hotchkiss which fired 13,2x99 ammunition.
The Germans used their own 13mm weapon in form of the MG 131 which fired 13x64 ammunition.
The Italians and Japanese used their own versions (Breda-Safat and Ho-103 respectively) that fired Vickers ammunition, 12,7x81.
The Soviets also had a 12,7mm weapon, the DShK which fired 12,7x108 ammunition.
The US M2, as a comparison, fired 12,7x99 ammunition.
The French used their heavy MGs as primary armament of light scout tanks and armoured cars as well as AA mounts both on land and on ships and France fell before they had a chance to develop their weapons further.
The British used their .50 Vickers as flexible armament on airplanes and as primary armament on some light tanks, but found that 20mm autocannons, which had a wider range of ammunition types were more effective airplane armament and that light tanks and armoured cars were better served using 2pdr AT guns, which penetrated more armour.
The Swedes and Romanians used their 13,2mm weapons as aircraft armaments and the Romanians also used it as an AA gun.
The Soviets used theirs as an AA weapon and heavy support infantry weapon.
The Japanese and Italians used theirs as AA weapons and aircraft armament.
As you can see, most nations had a weapon in the range of the US M2, with their own ammunition and standard. Thus they all had production ready for their own weapons and no need nor any time to copy a US weapon.
Just to add to the discussion, it's worth noting that during the Cold War, the Soviets designed their infantry fighting vehicles in part around defeating a .50 cal bullets. Their BMP series of vehicles were specifically armored to withstand .50 cal across their frontal arc, but were theoretically vulnerable to the bullets from the sides and rear. Although actual quality of the armor could vary a lot depending on the factory, metals, etc.