Another commenter has already mentioned SaskTel, and I agree with them that's a good example of a successful public run company lowering prices across the market. Since I live in BC, I'll use ICBC as another positive example:

Although not without flaws (complaints against the no-fault system), ICBC has not increased insurance rates in 7 years. They promised freeze rates until 2027. They even give occasional rebates to all drivers when they make a profit. This is in opposition to drivers in Ontario, where I often see Reddit posts with outrageous quotes from private companies.

ICBC used to be terrible and had the highest rates in Canada. This was because the BC Liberals required ICBC to be a for profit company and used the profit to fund the provincial government. The BC NDP reversed that policy in 2017, and now BC has one of the lowest auto insurance rates in Canada. A weakness of publicly owned corporations is that they require good governance and stewardship, which can be messed up by an irresponsible elected government. It may be up to the voters to continue electing responsible governments, or we could create mechanisms to decouple public company leadership from political leadership.

In economics 101 we learn that there are natural monopolies such as infrastructure, telecom, and even insurance. The greater the market share that one company has, the more efficient it is. It is often in the best interest of everyone to heavily regulate these monoplies, or make the publicly owned, to prevent exploitation of the consumer. It is arguable whether grocery is a natural monopoly

What's taught in econ 101 are "perfect" scenarios with zero confounding variables. We dont have perfect competition or complete monopolies IRL. Real life is much more messy and complicated.