Has anyone made a case for layering capitalist and socialist ideas on top of each other, seeing as that's what actually works in reality?
Insurance is a great example of that. A profit making company (capitalist outermost layer) that administers a money pool (socialist inner structure) that people join voluntarily (capitalist at the individual level) to manage risks.
Here's how you fuck that up: insurance companies convince government to add an extra layer; coerced standards (aka "regulations"). This makes it very difficult to break into the market as a startup. Then the existing companies can easily charge too much, because they haven't got any competition (and can make deals with their existing competition not to undercut each other). Next, the insurance company cartel can get government to force people into buying insurance for various risks, and present it as "keeping everyone safe".
Supply side distortions (standards that prevent new entries to the market) and demand side distortions (forcing all people to buy something at fixed prices) completely destroys the market, but it's apparently easy to convince people that this is free market capitalism in action.
But if everyone is forced to buy and there is no competition, how is that different from socialism? The method is different to outright socialism, and complicated: 5 layers of socialism and capitalism nested inside or across each other. But what's the outcome? Very similar to what happens in total socialism: friends of the government run massive companies that don't have any incentive to do a good job.
What type of insurance are you talking about? If you are talking about auto insurance, most states in the US require people to have auto insurance if they want to drive. However, I see a very vigorous, competitive auto insurance market. If you are talking about health insurance, that is a big mess in the US. The problem with healthcare in general is that the biggest customers are either chronically ill or dying. Also, in emergency medicine, there is an ethical mandate to treat first. It's not practical or ethical for a healthcare provider to secure means of payment in the middle of an emergency. Most times the indigent or underinsured end up not paying the bill. Therefore, the healthcare providers are forced to raise their prices and try to make up for it by charging more. It just ends up being a feedback loop where the amount the healthcare providers charge keeps rising. In my opinion, the healthcare market is going to end up being socialized no matter what system you try.