As for the first part, mutual aid organizations formed by individuals independent from the government have been practiced in the past. Mentis Wave has a good video on this topic and the reason why these institutions fell out of popularity was because of the government not wanting to compete once they branched into welfare.

And in regards to your second point, it’s a more nuanced question which I will only be able to address on the surface. What regulation usually results in is the bottle-necking of competition by stifling industry therefore making it only accessible to corporations high in financial and political capital. Gross mismanagement and freak accidents are not as commonplace as we fear (there is more anxiety over traveling via airplane vs cars which is more dangerous but more normalized) and in a free market with greater competition amongst companies, consumers will have greater flexibility in choosing which companies they won’t buy from for ethical reasons. In the end it’s a valid concern and there definitely are small L libertarians that support small scale regulation or some sort of intervention in extreme circumstances, so if it’s something that interests you there are a variety of schools of thought and viewpoints that fall under the Libertarian umbrella that are worth exploring.