is it legal to wear headphones when biking?

Probably not, in most places. I fail to see what difference it makes: people do it. Hell, I do it on occasion, and I don’t like wearing headphones when I’m riding.

riding a bike is already dangerous, riding with headphones is doubly so

Sure, but that’s orthogonal to laws and their effect on behavior. People ride with headphones, dangerous or not, legal or not. I’ll was honestly asking what difference a law makes when people obviously do it, and in areas where I’m sure it’s illegal. Hell, I’ll see people driving with a headphone in each ear, and I know for a fact that’s illegal in at least three states.

In-ear headphones can surprisingly improve spatial awareness by reducing the wind noise at certain speeds.

That assumes they are not playing anything though.