How can we make the market more competitive while also starting up crown corporations?

I think it’s important not just for the consumers benefit but also the employees working in that industry. If it’s purely a profit motive then you get things like poor wages and working conditions where the employer can use “competition” as an excuse to keep wages low and reduce overhead by not prioritizing things like safety and environmental sustainability. When people have the option of working for a crown corporation that does prioritize safety, sustainability, and good work environments then private industry has to be able to offer comparable compensation and work environments to the crown corporation. The crown corp has an inherent advantage of being able to operate in a profit neutral manner, while the private industry has to be able to actually do something better than the crown corp to be competitive.

It’s good to have companies that do not solely view profit as the goal.

Agreed! Though, I personally am hesitant to use the term "company" — I'm not sure exactly how you are defining it in this context. Perhaps "organization" would be better?

It’s much more difficult for the costumer to improve the company without buying shares.

Even then, it's a bit of a stretch. Not to mention the bias that it sets by requiring capital to have a voice.

Crown corporations have shown to benefit the public by serving everyone in the province, lowering costs for costumers, keeping the profits local, forcing the market to be more competitive and listening to the government that the people vote in.

It depends on exactly how it is done. For example, I would argue that the way insurance in British Columbia is set up with ICBC is an absolute moronic disaster. I am also very hesitant to have taxpayer money spent on something that may well be a sinkhole for money. I think Canada Post is done well: any profits that it creates go straight to the Treasury Board, it takes no government subsidies — even pensions are not taxpayer funded, it directly, and fairly, competes with the rest of the market. Canada Post is an example of how it should be done. ICBC is an example of how it should not.

I also support cooperatives as every member gets the same say.

Cooperatives have enormous potential, imo. They seem to be vastly underutilized, which I don't comprehend. I think they could be a solid consideration to combat intrinsic monopolies.