Nah mate, while there's plenty of bullshit in the audiophile community, do not underestimate the difference headphones make.

Theres too much the average cheapo headphones get wrong, theres instruments you would never have noticed in songs because the headphones just lacked that resolution. The spatiality of the audio too, its not just on your ears or in your skull. The difference after you try decent headphones is night and day. You quickly run into exponentially diminishing returns, but the first decent headphones you try are a pretty big leap.

Its already a feat to make a good wired at that price point, but theres at least good contenders in this price bracket, you could easily get your forever headphones in this category for wired. Especially if you are not an audiophile

Theres no way you squeeze enough value out of 20 bucks to make a good wireless can. You need good drivers, good build for the headphones (well engineered driver housing and even the earpads and screens above the driver matter a lot), you need to tune them right, you need to have a passable BT receiver, a passable DAC, a passable AMP. On top of it you need to have a battery and probably some circuit to control it all.

For wired cans at least you don't need to ram all the electronics in, you only have the first three hurdles and some wired cans in this pricerange are shockingly good. While for wireless you start running out of your 20 bucks just assembling the electronics.

A lot of other things in the audiophile world? Yea, I agree, a lot of it is not going to register to most people, especially now that sound output on most devices is good enough where you don't really need a dedicated audio stack, if your headphones can be driven by the output.

But if you pit me in a pepsi challange vs 20 buck wireless phones even vs my daily drivers (or something else, decent, from the sub 35 buck bracket), let alone my at-home cans (or, basically, anything from the 200 buck wired bucket), ill take that bet any day of the week and even for random people I bet they could easily tell the difference if you just let them blind A/B test on just a few songs even if like short samples.