core troops were simply what made up the most of your army. So they were typically the cheapest economically to muster.
elites and specialists had better gear and/or training so came in fewer numbers because they were economically harder to muster.
The core of many medieval armies were knights and men-at-arms, not cheap peasants, because that's what those societies were designed to accomplish. (Even in the case of Great Britain, who did bring peasant longbowmen, those peasants had been training for most of their adult life to be experts at using a longbow - society had been reorganized to provide longbowmen.) Similarly, the shift to pike squares and then tercios and etc... wasn't because that was cheap, but because societies bent treasure and industry towards supplying those things for battlefield use. Warfare is a competition between different societies at the level of military doctrine, technology, and the logistical and economic factors which make fielding those armies possible. Losers get conquered. You don't bring things because they're cheap - you rearrange your society to provide the things that will stop aggressors from conquering you as a matter of survival.
I would prefer a rebalancing where core is superior to non-core choices on average, and you bring other units to diversify your abilities, not because they're strictly better.
Ideally, a 25% core army should beat a 0% core army all the time, by design, and possibly all the way up to 50+% core being a generally superior choice. Then you can eliminate core as a category, and people will bring the intended core units because they really are the backbone of the army. Core should be a functional description reflecting functional choices, not an arbitrary category assigned by fiat and filled with overpriced junk.
Just because I'm on the Legal Team doesn't mean I know anything about rules or background in development, and if/when I do, I won't be posting about it. All opinions and speculation are my own - treat them as such.