I never bought this argument - the majority of the ammo usage 'in the field' would still be for the units Machine guns and support weapons
90% or more of shot fired through this analogous assault rifle would like the bolt action rifles of the day likely be fired during training
The major powers were producing millions and millions of rounds every week during WW2 and for that matter WW1
On SLRs The USA, Russia, Germany and even France (MAS 40) were in 1940 on the verge of issuing SLRs to their troops
Russia had equipped 1 million men with SVT40s by June 1941 and would have continued to mass produce them had not the need to build the simpler to build Mosin Nagant rifles which could be built in much greater numbers to replace losses incurred during Barbarossa (Indeed the Mosin replaced its replacement!)
The USA went to war with the M1903 Springfield and it was not until 1943 that production of the M1 garand and the M1 Carbine (which IMO was the best individual firearm of WW2) began to equip all front line units (Chemical Mortar and Engineer units @ Torch were still armed with the Springfield!). The defenders of the Philippines and the Marines on Guadalcanal fought using the old rifles (it was the reinforcing US Army divisions that first used the Garand in combat - the Marines re-equipped when they went to Australia).
If there was an issue with supplying enough bullets for Assault rifles then it was not to do with the Assault rifles it would be an issue impacting logistics that would be larger than Assault rifles over Bolt Action Rifles
Plus all those early Russian self loaders had issues with not being as robust or reliable in the field as a Mosin, it actually made sense to produce and issue a bolt action as it was ultimately more reliable and if they wanted infantry fire power they had all those handy SMG's on issue. The Germans fielded a lot of G43 and STG44 rifles even though the country was literally being burnt to the ground around their ears.