Exactly. Doctrine is what mainly pushes weapons development not necessarily what the enemy is doing. It's only when doctrine fails in the face of enemy action that urgency becomes an issue. And that's why the repeated answer of, "well the Allies will just counter with their own" isn't always correct. It was plain to see the Nazis were ways ahead of the rest of the major world powers in fielding those two types small arms and the Allies didn't match them automatically with similar designs because they didn't see the need. And the same could happen with jets or anything else as long as one side is too convinced it's way is the only way.
Doctrine changes to match changing circumstances - and in this case the British Army went back to something close to their pre-war doctrine right after the war (indeed, they're still holding it).
Don't drink the nationistic cool-aid. All magazine fed light machine guns / automatic rifles were obselete after the MG34 was revealed. The Bren and its Czech brothers included. Now that same wasn't true for the heavy water cooled machine guns like the Vickers, the American M1917's, and even the Soviet M1910's. Being water cooled means those had a sustained firepower edge no GPMG can match.
Really? So that's why I used to carry around a magazine-fed LMG (and indeed why they're
still in use today). Belt-fed weapons give you a somewhat enhanced rate of fire, but only so long as you can keep changing the barrels (in reality the barrel heating rate has far more bearing on rate of fire than the magazine or belt feed).
You seem to have a major problem with understanding what a machine gun is there to do. Fundamentally it's all about suppressive fire, and doing so by creating a beaten zone through which the enemy cannot pass without sustaining excessive casualties. The density of rounds flying through the beaten zone is critical here - this can be attained by very high rates of fire (the MG34) at the expense of the rapid recoil making the beaten zone very large since the gun is hard to control, or with much lower rates of fire (FN-MAG/Bren) allowing much better control over the gun.
Unless you're firing at exceptionally long range (map-predicted fire essentially - the province of water cooled machine guns because you must sustain it for a very long period of time), the reality is that most armies prefer to go with the lower rate of fire route, and as such in most cases you don't use a lot of ammunition - 3-5 round bursts every few seconds is the British current doctrine for using a GPMG in light role, which is the LMG replacement. SF role is the Vickers replacement, for which it has never been entirely satisfactory for barrel cooling reasons.