Instead, let’s cut the red tape and remove the barriers in the parts of the economy that are not following the rules of the market. Do that and prices will decrease due.
Experiments with collectivisation have failed to serve the needs of the capitalist class, for sure. It's why they use union busting, sanctions, coups and invasions to cause such experiments to fail.
Profit is a much-misunderstood concept. Private profit is the best way discovered so far to align incentives for those who produce. As Adam Smith said, "it is not from the benevolence of the butcher, the brewer, or the baker, that we expect our dinner, but from their regard to their own interest."
A system that disregards profit and instead relies on some other incentive structure can work in small groups of people for short periods of time; but eventually those other incentives (usually some kind of familial love, a sense of group belonging and solidarity, or similar) run out of steam, and it fails to scale both in size and time.
To paraphrase Churchill, free-market capitalism is the worst system of economics, except for all the others that have been tried.
> Nationalised transportation and medicine works in many places
Only for a certain definition of "works". The Seoul Metro, owned by the city of Seoul, for example, is a huge network of clean, efficient subway lines that millions ride daily to get places. It's really quite nice to use. Under the hood, however, is the fact that they lose a quarter of a billion dollars every year, and is subsidized by taxpayers from around the whole country, most of whom don't even live in Seoul.
That could be achieved by pursuing production for use, not profit. Municipal collectively ownership works quite well for utilities (like ISPs) and housing. Regional collective/co-op food production can work well too. Nationalised transportation and medicine works in many places. And so on.
It only takes the workers to be sufficiently well organised to obtain the means to produce in this way.