If you are staying in a hotel, you don't need to go to a police station. Otherwise, the person you are staying with should be able to help you find it.
> The process is quite slow, the queues are long, and the officials are visibly irritated every time you come and wake them up from their slumber.
Not my experience, but maybe I just got lucky.
> Then there are people flying 3-4 times per week to Hong Kong or Seoul on business, technically they are required to register every single time they enter China.
Those people presumably have some kind of permanent residence. It would be news to me if that required re-registration after each re-entry.
M-visa holders, business visa holders are required to register with each entry, which is surprisingly misaligned with the purpose the visa entails (visiting fairs, business meetings etc).