There is no “mp3 quality”, as that can vastly vary depending on bitrate. And what is HD quality music supposed to be? I bet you couldn’t reliably differentiate high quality mp3, CD audio and completely uncompressed wav in a series of blind tests.
Yeah. Headphone jacks are essential only for people who own nice wired headphones they want to continue using.
Try a high Bitrate mp3 and the difference becomes a pure technicality.