reading tofu quoted Plant Partners by Jessica Walliser
As mentioned at the start of this chapter, tilling is a destructive process in many ways, but for some cover crops, tilling them under is the best way to ensure they're killed and won't resprout. Tilling also incorporates the cover crop residue into the soil where it can decompose, release nutrients and provide food for soil microbes further down in the soil profile.
Got some great replies to my question and the author also mentions it later. They call it the tilling trade-off.