I work in a medical insurance center in a prefecture-level city in Anhui. Our medical insurance center here should be similar to the medical insurance farmers and offices you mentioned. They are all responsible for medical insurance for urban workers and residents. Your place should also be responsible for the new rural cooperative medical system. There is no merger here, and it is said that it will be merged soon.

In fact, you don't have to deal with patients to work here. This is the administrative department of the government and belongs to the Social Security Bureau. It is divided into several departments. We have medical department and special disease department, both of which are related to medicine, and the rest are office, finance, statistics, computer and so on.

Even the medical department and the special disease department don't yell at patients, but are mainly responsible for the management of these two aspects. Branches of medical insurance centers in designated hospitals deal with patients.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.