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.