No, it really doesn’t. Phones run on batteries and continuously listening to and streaming audio would cause them to quickly die.
Maybe they actually do? For example, the 2017 version of the Nokia 3310, according to Nokia, can have calls of ~22h. And that's for a small 1300mAh battery. So it's technically possible to stream audio for a very long time. Maybe smartphones are doing the same in a very low-powered stand by mode?