That just means your phone's or PC's DAC is crappy compared to the internal one, and any other headphones would sound just as bad.
I have an older pair of JBL E55, which are about 50% cheaper than yours, and on a modern phone they sound slightly better on wire than on wireless, presumably because their internal DAC is mediocre.
I have new MBP 14', and even external fiio E10k headphone amp. They work great with my Sennheisers HD 650, but suck with WH-1000mx3 compared to internal AMP.
I use my xm3 daily and don't notice a difference. I use both methods of connection because sometimes it's quicker to just plug in on some devices, and others it pairs right away. Love these headphones.
Those Sony headphones do processing to the signal regardless of whether you're using wireless or a 3.5mm. They can still make sound with no power but it feels more like a backup in case the battery is dead. It seems like a sensible design decision given that most users will want them turned on for noise canceling even if they're wired.