Heroes 5.5 WarGame Edition - Tactical Edition.

After that, they began to reproduce at an alarming rate – despite all the wizards' attempts to get rid of the new scourge.

They couldn't separate the boys and girls into different enclosures, and also the "wizards"...

Orcs have no magical abilities. And absolutely none (ignoring the lore of Heroes 6-7, where orcs could cast spells, which critics naturally can't accept).

What does this follow from? Magic in Ashan, it seems, is to some extent a connection with the elemental dragons, and nothing prevents orcs from having such a connection.
And the shamans definitely have it! The Daughters of the Sky can quite easily unleash a chain of lightning, which cannot be explained by pharmacology.
Orc warlords don't cast spells (within the context of the fifth game), but it seems that it's not about a fundamental inability. Perhaps their leaders are simply not smart enough (unlike the shamans, who devote their entire lives to connecting with the Father-Sky and Mother-Earth, and not to fighting for power and brawling with the prospect of becoming the leader of the clan).

Regarding blood, I agree with SRD, but not entirely. Although orcs are the result of experiments, I personally haven't seen any information that within a single orc nation, there are individuals obtained from mixing with different bloodlines. This is the case with centaurs, goblins, etc., but not orcs... If that were the case, it could create a lot of problems: difficult childbirth, various mutations, and who knows what else. Genetics is a complex thing.
Therefore, I find the explanation that shamans, with the help of "pharmacology," can "boost" the parameters of orcs (using the characteristics of their blood) to be more than acceptable.