This is a very good question, even though some may view it as naive.
Doping in source / drain region is required mainly to provide a low-resistivity connection from the metallization / contacts to the channel - that's why it is made as high as possible (up to a solid solubility limit).
Very often, source/drain regions are silicided, i.e. converted to almost metal-like material, at least at the surface of silicon, to reduce the resistance.
Also, people are working on metal source/drain, for that purpose.
To the contrary, channel doping is used mainly to control the threshold voltage of the MOSFET, so its doping is selected with thereshold voltage being the target.
Open any book on semiconductor devices (for example - Physics of semiconductor devices by Simon Sze, a classic), and you will see charts showing Vt dependence on doping (and other parameters - like gate oxide thickness).
That being said, doping profile in a MOSFET is engineered to meet many other requirements, like leakage (drain to substrate, like GIDL effect), or source-to drain in the off state (DIBL effect), mobility (retrograde profiles), etc.
In modern MOSFETs, doping is not uniform, and is created by several different implants.