There are numerous more equitable models that China could have built its system around. For example, they could have built their market economy based entirely around worker-owned co-ops. Co-ops can compete just fine in markets

Well, you'll be quite pleased to know that a significant part of China's market reforms, has been the development of worker co-ops as a significant part of its economy.

Why couldn't China build a market economy, but just have a hard rule of "no one is allowed to amass more than X amount?" Even if people couldn't hoard more than say, $100 million, that still gives people plenty of incentive to start new businesses, get an education, work hard, etc.

Because they established markets to bring in foreign capital investment. Foreign companies, wanting comparatively cheap labor, were encouraged to partner with Chinese (usually state owned) firms, to access said cheap labor. Over the decades, the Chinese have taken this foriegny capital, invested it in its own domestic economic development, and encouraged the establishment of worker co-ops, in place of foreign firms. Huawei, for instance, is a worker co-op, and came out of the capital generated from partnerships foreign telecom companies.

Now, a private, national bourgeoise does exist, and people have gotten very rich. But China also puts those people on an INCREDIBLY tight leash. The reason they don't limit the wealth you can amass, is because they wouldn't want to limit the generation of capital that could be spent on economic development goals. Instead, they use the slightest steps out of line to seize those rich people's wealth for thepublic good.

I'm interested specifically in the billionaires. So why the billionaires?

Essentially, the TL;DR is that billionaires in China are a byproduct of market reforms designed to generate domestic capital, and development. While they're there, and their presence creates contradictions, they don't have the ability to impact politics the way they can in the west.

The Chinese state, being a socialist state, seeks to manage the contradictions of market reforms, and funnel the gains from them for socialist ends. Those ends being the development of the productive forces (domestic industry, ending poverty, etc.), while also developing the relations of production, via state ownership of major industries, and encouraging the growth of cooperatives in the consumer goods market, and workers Congresses and party committees in nominally private businesses, to give workers a greater say in firm management.

I can't actually answer why they don't set a hard limit of how much they will let some one accumulate or as for why they didn't use coops. Both of these are counterfactuals that would be difficult even if I knew all the internal discussions. For example, you'd have to look closely at Deng's policies and the subsequent three represents during the early 2000s to see what the discussion around coops was. Hard to say what the thinking was that precluded coops from the discussion.

It's easier to say what they are doing and the policies they are enacting. I believe they have a goal of reducing inequality with a goal of a Gini index of .35 by 2035. They are focusing on a common prosperity goal. This has led to increased donations and contributions from the wealthy to social causes. With the common prosperity project, they hope to increase the middle class and reduce the rural-urban divide as well. I think there are several other goals.

I don't see setting a hard limit on whether or not one is a billionaire contributing to these goals and then runs the risk of creating resentment of a particular class that the party needs to grow their level of prosperity.

Edit: Prior to the 90s, there government supported state-owned and collective enterprises. But they weren't growing quick enough to meet the needs of the CPC.

Meanwhile, the growing number of entrepreneurs were gaining power, but no access to representation. So the CPC decided to bring them in to the party. This would reduce the likeliness of a counter revolution.

Theoretically, coops struggled with massive, capital-intensive investments. They can't scale or absorb risk because their capital is in the form of worker's equity.

When coops fail, it can be doubly devastating. Workers lose their jobs and equity when the firm goes bankrupt. Just as bad, though, there can be a prolonged declined as the coops would go under they would slash their pay to keep the dying firm alive.

Coops seem great when the economic engine is humming along, but if you are looking for rapid growth, you need large capital investments and the ability to fail quickly or massively succeed.

Not even a little believable, you're either some sort of deeply incompetent fed or profoundly lonely, maybe both lol