Have a government brand of goods/services that have a set max price so there is an affordable form of most goods

While the idea of a government brand with maximum price caps sounds appealing, history has shown us it can lead to potential complications. For instance, the Soviet Union had a centrally planned economy where the government controlled prices. This resulted in chronic shortages of goods, poor quality, and a lack of innovation due to the absence of competition. How would we ensure quality and innovation in a system with government-set prices?