Marked reduction in audio quality, audio lag, lack of responsiveness, the need for another wireless devices that has batteries to recharge (that are not user replaceable), and if you live or work in an urban area wireless interference from other users also using Bluetooth is a fucking nightmare.
Wired headphones just work, every time, dont need batteries, and dont suffer from wireless interference. I use bluetooth in my car, sure, but my walking headphones are wired (and I'm not going to replace what already works), and my home audio and truck systems are not wireless.
The better question is, what is wrong with having options? The samsung S5 had a headphone jack and still had both a removable battery and was water proof. The removal of the jack is driven by greed, nothing more.
Which means placing more wear and tear on your USB port, along with strain on the port when the cable moves. USB isnt nearly as durable as the 3.5mm jack was. And at least in personal experience, those USB dongles are completely hit and miss on whether they work properly, and have a tendency to fail after a few months of usage. ESPECIALLY the apple ones. And of course you lose the ability to charge the device and use headphones at the same time.