The first part also happens on desktop thanks to DRM, unfortunately. Like on Android, it can be worked around, but it's a massive pain to do so.

I'm curious about the second part, though. How do carriers influence the call recording feature on your phone? Is it because you run a carrier ROM or is there some kind of integration with the mobile network/SIM card that I'm not aware of?

See https://source.android.com/docs/core/connect/uicc. UICC is the software component of a SIM card.