But also, I don't think it's either/or for most people. I use both wired and wireless headphones all the time depending on the use case. Wired sounds far better and is more reliable, wireless is more mobile. Different use cases.
I can point to the shelf with my Sony wired ANC ear buds, which I bought years ago specifically for ANC during air travel, in the era when I would use my iPod and later an iPod Nano. The ones I have are the second pair, bought after the first was accidentally left on a plane. I think they were different product generations, a few years apart. These are so old, they are purely stereo headphones. Microphones for duplex audio hadn't become pervasive yet.
These stick in my ear with little silicon flanges and have a part that sits outside with the microphone. Then there is a small control module sitting at the junction of left and right ear wires, which holds a AAA battery and has a power switch and a pass-through audio button (which always seemed more gimmick than utility to me). In their active mode, they also don't demand much of the source device.
This has been a thing in wired headphones since at least 2007 lol
even some of the cheapest in-line remotes that only have a single button will let you change the track by double tapping it
if you dont have an in-line remote then theres also the option of using a key remapper app (probably not on iphone) to let you change track by long pressing the volume buttons
However, the noise cancelling gap is real. I'd kill for wired IEMs with an inline battery + buttons, and noise cancelling mic & circuit in the earpieces.
Closest is the Sony cans, which have wired mode (ie: they have a tiny jack, so you can use them passively) but I don't think they cancel noise when using them that way
The utility has dropped tremendously though, now that headphone jacks have disappeared.
Would love to have a pair of "direct-USB-C" Etymotics.
I use wireless headphones and in fact never use this feature (I have it disabled). Too unreliable when there's a large screen with a big pause and skip button within reach.