FYI, that's interference. Wi-fi "randomly" disconnects for a few seconds due to interference just as often, but you don't notice, because 1. the OS hides short disconnects, and 2. most protocols you use are TCP-based, and so use retries. (If you were doing something involving UDP streaming, you'd notice.)
Bluetooth audio, on the other hand, is a realtime protocol, which just drops stale packets rather than trying to retransmit them. Drop enough packets in a row, and the carrier thinks the device has gone out of range and disconnects it (as the alternative would be boiling your battery by turning the antenna gain up to infinity, as sometimes happens when cellular baseband misbehaves while ranging.)
> Gestures and voice are simply not as convenient as buttons on the wire. If I tap the thing in my ear, it tends to get shoved further into my ear and may still not register
Have you tried the AirPods Pro where you squeeze the stems? They're essentially buttons.
> Crucially, there isn’t a single problem above that occurs when using wires.
Put on your wired headphones. Sit down (e.g. on the bus.) Now try taking off your shoulder-strapped bag to hold it in your lap, without first taking out your headphones.
Or: try to change your shirt while keeping your headphones on + playing. (I know, unusual thing to do, but I've changed my shirt with wireless earbuds in without a thought.)
Or: get up and go to the bathroom, while continuing to listen to the livestream you're watching on the desktop PC sitting on your desk, without missing anything. (Provided I'm at home, I can usually get about 40 feet away from the Bluetooth source before my wireless headphones disconnect.)