Can one purchase train passes in China, or is one supposed to buy tickets one by one?

It's hard to prove a negative, but as of 2021, no, there isn't.

The closest is the China Rail Pass (?????), which is a reloadable prepaid card that lets you take most major bullet trains without advance bookings. However, the card offers no discounts, only convenience.

While there isn't anything like Eurail or JRPass AFAIK, from last December prepaid passes and a limited 30-day pass have been launched for two routes. But they are really for commuters and business travelers, not tourists.

For Beijing-Shanghai and Chengdu-Chongqing, you can buy a prepaid pass with 20 trips within 90 days for a specific interval. The price corresponds roughly to the average price of usual individual tickets (which are dynamically priced for these routes), so you can save some money if you travel during peak times or high demand seasons, but not if you travel during low-price times.

For Chengdu-Chongqing, a 30-day pass is also offered, but the maximum number of trips is limited to 60. If you use all 60 trips allowed, the price is about 40% cheaper.

Reservations are at all times necessary and subject to availability.

Not really, probably because almost all China Railway trains require a reservation under your real name and a pass really doesn't make anything more convenient. Some suburban lines used mainly for commuting now allow riding without a reservation, but the vast majority of trains require reservations.

So a pass wouldn't really help out in this case, because it doesn't quite save the hassle. You still need to make a reservation every single time. This is little better than buying a ticket every time, so it's not really worth creating a separate pass (and separate booking process) for tourists.

Finances may also play a role here. The railroads in China are already much cheaper than their counterparts in Europe or in Japan, particularly the non-express local lines. A comfortable "soft" sleeper car from Shanghai to Beijing generally costs around 400 yuan, and the modern high-speed rail costs about 500 yuan. If you can stand sitting in an uncomfortable seat (which is fortunately air conditioned) for 12+ hours, you can even do it under 200 yuan. So, I really doubt that you could go much lower than that, so a potential railway pass would likely offer little savings. The attractiveness of such a potential pass is rather minimal, and plus all the required work on the CR side, this easily explains why China Railway isn't keen on such a pass.