Competition will continue to keep prices down. Just because people have a new source of income, doesn't mean they that will become more likely to buy overpriced goods.
That's an incomplete statement, because it doesn't quantify the effect. Will the effect be zero, or will BI be priced-in (higher prices, lower present-value of BI)?
US college tuition and housing prices increased dramatically, because of decreased consumer price discrimination driven by low-barrier loans.