Well no, i think it is the opposite. Larger companies exist and play unfair, exacly because no regulation stopped them.

No. Mega corporations currently only exist because of regulatory capture and political maneuvering to get that big. They are different from a "natural monopoly" that can come into existence in a new market segment or by new invention/process/production. Also, just to note, not all monopolies are big. This happens quite often in very niche products or services. So, I'm not generally anti-monopoly.

The whole point of regulatory capture is to AVOID competition. The math works out for some companies to dump millions or billions into pushing for a system that only they can navigate with an army of lawyers. This doesn't just happen in the US.

Looking at Healthcare in the US is actually a very good example: look at the results of the ACA. We have less doctors, worse health outcomes, much poorer treatment, and, insultingly, much higher prices for all that awful BS. This is exactly an example of what I'm referring to.

Trying to force private health care into a state run system isn't the church way to "fix" the whole system. You must tear it all down and live with some chaos until the people who will pay for services and the service providers come to agreements on what things should cost, as in, letting a free market work to: improve quality, reduce costs, eliminate waste, and cater to customer needs.