The purpose of an economy is to decide what to output, given the unlimited human desires but limited resources.
If there was a law which gave 100€ to every millionaire, we would be supporting millionaires? Isn’t that good? No it isn’t, just “supporting someone” isn’t good economic policy, it must support outputs that will most benefit the population.
That’s why for it to be remotely viable it has to be self-sustained. Which means that they would not be able to operate further if there’s not enough demand or the competition from the private sector is more efficient.
If you want to support delivery drivers you make laws regulating their job. If you want to support restaurants you give them subsidies or change the laws surrounding them.
Capitalism is good at making efficient use of resources. However it has many failures. The purpose of governments is to fix those failures (for example the exploitation of workers, and monopolies).
If you just make a government-backed company (that doesn’t need a profit to keep going) compete with private companies that need a profit, it must be because the service benefits the whole population. Examples: healthcare, education, communication, water.
Not that not all necessary services need to be provided by profitless government corporations. For example, food and electricity is also needed by 100% of the population but they are also resource-intensive. Therefore they’re usually ran by private companies with heavy regulations/subsidies.