I don’t think the protocol should bear the full burden of gas costs. But a discount, kind of like what Matcha offers for small trades, might be an incentive.
For example, gas costs matter for people lending/borrowing liquidity in the 100s or 1000s. A small discount that makes Aave cheaper compared to competitors could actually drive more usage/revenue if the gas discount is well known and publicised. Smaller fish will choose Aave over Compound because of the immediate savings via gas discounts, which will ultimately increase usage.
That said, this is not a sustainable solution on ETH 1.x so long as gas costs continue at current rates. Maybe a short/mid term solution till L2 solutions are more reliabl.