Wait a second.
It is a stated fact that the Imperium has lost the capability to produce certain engines, certain weapons, and even certain vehicles and starships. That is a given.
And yes, it is also a stated fact that the Adeptus Mechanicus makes it so that it's a very long and difficult process for new designs, etc., to be approved. See, for instance, the Lucius-pattern Baneblades.
That having been said, I'm pretty sure that the Imperium isn't unable to produce the overwhelming majority of the war materiel it needs. Its manufacturing/industrial base has ensured that a military force responsible for the protection of roughly a million planets has, by and large, been adequately equipped for ten millennia. We're not talking about a force barely able to march to war or lacking even guns in necessary quantities, like the Czarist forces of World War One, either. We're talking about a largely mechanized force that almost always deploys as a "combined arms" army, with artillery, armor, etc. A force that always arrives by way of interstellar transport.
The limitation of the Imperial Guard never seems to have been the Imperium's unwillingness or inability to outfit it with tanks, artillery, gunships, or what have you. Its only two real hindrances have been:
1. The Warp, which wreaks havoc with the modes of transportation and communication that the Imperium fundamentally relies on... since it also happens to be Hell, and is the stronghold/essence of the very powers that want to see the Imperium destroyed.
2. The fact that the dystopian existence that Man exists in seems to pervert sanity and reason, and ensures that individuals with little to no concern for human life rise to power.
This has led to a military where advanced technology is hindered by pointless superstition and ritual, is wasted on often archaicaly obsolete and self-defeating tactics, and is utilized by frothing madmen waving holy books and chainsaws. I have yet, however, to see a Codex or a book say something as blunt as "The Imperium can't create enough Valkyries, Leman Russes, Chimeras, Hydras, etc., for the Imperial Guard." I'm not saying such a statement doesn't exist anywhere... I'm just saying I would be shocked if that were the case.