Not quite true.The secret is in the name. Either Bren Gun Carrier or Universal Carrier. It is not a vehicle to fight from but one to deliver and supply the fighting companies. Normally the weapons are dismounted for use. The Bren in the front was to react to ambush so the Carrier could drive away. The use of Vickers GCOs on jeeps etc. later in the war were for exactly the same purpose. Yes the SAS etc. in the Mediterranean used them as taken off aeroplanes but in NW Europe they were the ground use version with butt and bipod for dismounted use and stored on a pintle mount on the vehicle to put the enemy's heads down while the light vehicle runs away. Doctrine was VERY clear that the Carrier was NOT to be used as an offensive armoured vehicle.
The Lewis were needed for light AA fire (especially small navel vessels and merchant ships etc.) Even the Home Guard more often got US .300 ones sold from US stores as .303 Lewis went to the other users (with many exceptions). The Home Guard quickly developed a .300 ammunition train for .300 based platoons separate from the .303 ones.
The Bren was specifically chosen as a better weapon for the job than the Lewis which is why the Lewis was withdrawn. The Lewis has no quick change barrel so is not able to maintain MMG fire whereas a good Bren team with tripod and spare barrels can do so, following the given protocol on rates of fire. Also the Lewis only comes on a bipod (pintle mounts on ships etc. were not army issue). So cannot fire on fixed lines or indirectly. A good WW1 LMG and still a boon to the Home Guard but not issued to the army as a whole but rather to the Royal Navy and Merchant Navy. BTW the Vickers GCO had the same issues plus a rate of fire that emptied the drums in seconds. Hence their availability for light vehicle mounting.
However, in the context of the BEF a general release of Lewis to second line uses would indeed have been welcome at times like when the cooks & clerks were reduced to picking up abandoned Belgian Mausers etc. to arm themselves to plug the lines in 1940.
The Carrier Plt was to fight, mounted or dismounted. As a mobile fire base, recon and gap filler for the inf Bn CO.
It was evolved from MG tankette doctrine, (a Vickers gun) and not as a carrying LMG.
The Carden Loyd is the bases to the whole carrier concept.
“Considered a reconnaissance vehicle and a mobile machine gun position, the Mark VI was the final stage of development of the Carden Loyd series of tankettes.
The Carden Loyd tankette was the prototype for the Universal Carrier.”