Why battery charge C rating is usually lower than discharge
This is done by design, this type of battery is designed to have a low internal resistance in order to be efficient when driving high current loads. But it usually can't charge as fast without reducing the battery life because the electrolysis effects will decompose some molecules in the electrolyte and usually release a gas hydrogen, CO2 or other, which can't be recovered.

This also depends on the application, it is actually recommended to use a lower discharge for some application in order to increase the delivered power, by minimizing the dissipation in the battery due to the internal resistance. This is the case in IoT application where batteries with higher power density are used. Those batteries usually have a very high internal resistance (1 to 300 ohm) and will dissipate internally if the curren tis high, in this case the battery is used in conjunction with a super capacitor which is slowly charged by a current source providing simultaneously a high current in an intermittent basis and a low current voltage source for maintaining the sate (RAM RETENTION) in the device. in those application it is beneficial to use a higher power density because IoT devices usually need to run for years and may also use power harvesting, but only need to use high power for a very short time when transmitting  data.