As someone who had to make sure that call audio was properly processed on a phone I worked on to make it match today's standards, I can say without hesitation: it's all three.

The codec you get can vary from okay to terrible; the way mobile phones are built these days requires you to do echo cancellation; and the environment phones are used in requires you to do noise reduction.

Just disable audio processing on your phone, feed the network with raw microphone input and notice the complaints from your interlocutors. I've been there :)

Something's gone badly wrong in your memory; landline phones intentionally drop important vocal frequencies and automatically prevent everyone from sounding like themselves. Cell phones don't do that and have always had much, much, much better audio than landlines.