Corporations don't regulate themself. Why would they choose to regulate themself if that means higher cost or less margin or less business opportunities (like selling assault weapons to civilian population) ?

Market can bring prices down if competing corporations in the same sector don't agree to set prices for the same range of services of products. That's it.

Self-regulation is conservative non-sense.

Self-regulation _can_ work... if the state is standing there with a big stick willing to use it if the market doesn't regulate itself well.

As a case study, take advertising in the UK.

The Advertising Standards Authority is a Big Deal. It can ban advertising on TV, in print, on billboards and online. Its decisions regularly make the headlines.[0]

It also has no statutory basis, it's a private limited liability company, and they receive no money from government.[1]

[0] An example from today, here's a news article about a ruling by the ASA concerning a tweet sent out by Burger King: https://www.bbc.co.uk/news/uk-scotland-49895800

[1] https://beta.companieshouse.gov.uk/company/00733214

In the general sense you're right however I think you're drifting into a philosophical point. Normally it makes more sense to let businesses have a certain amount of freedom to operate and only step in when necessary. The hard part is agreeing where "necessary" is. For example EU tends to have a different perspective to the US on when industries should be regulated.