Let me be a devil's advocate for a second: millions of tons were delivered to Murmansk and Caucasus via Iran:
That means that some of this tonnage could be used to maintain a military force of some size (naturally limited) on the Eastern Front. Of course, at the expense of materials and equipment given to the SU.
But in WWI they did. And as commented below "command" was not a necessity.2. Politics. The US never allowed foreign governments to command their troops in WW2.
Well, causalities in the Normandy were far larger than in Italy and no backlash followed. In general, given that US, Commonwealth, French and other armies lost nearly a million men on the ETO, I would call a usual idea of their sensitivity to casualties a little exaggerated. As historical events demonstrated allied armies which were parts of the coalition usually retained a very broad autonomy. Even a direct operational control was not always necessary and joint operations were carried out by mutual agreement between independent commanders. When an allied force was under direct operational control of the coalition its commanders usually had authority to protest or elude orders which they found contradicting to their national interests. Sure, collation war is always problematic, but those problems are not fatally insurmountable.There was enough political turbulence when the Texan National Guard lost a couple of thousand men at the Rapido river. Imagine the backlash if US soldiers had been sent forwards on the Seelow heights?
It demonstrated that Allied air force didn't need to be under Soviet operational control to operate from bases on the Eastern Front. It also demonstrated that supply problem could be resolved.The shuttle bombing using airfields in the Ukraine was a disaster.
Sorry for going off-topic, but "inaction at Warsaw" is a myth. And first and foremost Warsaw was a failure of Polish AK leadership to discuss and coordinate their plans with allies.The Red Army's inaction at Warsaw in 1944