> I think the claim was that the education market is (sort of) a market, at least in the sense that demand is driven to some degree by price.
In a market, price is driven by demand (and supply). If price is externally controlled (which isn't, then, a free market), then the quantity traded will be driven by price (it will be the minimum of quantity demanded and quantity supplied at the price.)
But, that's all irrelevant; the relevant relationship is that an external subsidy to buyers outside of the price exchanged between buyer and seller (which is not a price cut) increases demand and, thereby, both market clearing quantity and market clearing price (assuming the supply curve slopes in the usual direction.) The latter effect (increase in market clearing quantity) is usually the intended effect of a subsidy, the price effect comes along for the ride.
OTOH, there is plenty of evidence that loan repayment costs (and this has been generally been shown to be the case with deferred costs) are excessively discounted in decision-making, which increases the degree to which loans act like subsidies (in both quantity traded and price effects), but also decreases the degree to which subsidizing loan repayment acts like a subsidy (because it reduces a costs that is discounted in decision-making, reducing the effect of both the base cost and the reduction of that cost.)