> built in permission to disable AJAX after page load

Interesting, but consider this is a cat-and-mouse game. If you are the only one using this trick it may work for you, but I assume would be easy to overcome. (e.g. keep the page loading forever or until ads are loaded. Have the ads be J-free after page load, ...)

> website could play background music ... another tab could listen

You would need mic access from the other tab, but yes. If you send it over high enough frequency you wouldn't even hear it. You would just have a visual feedback that the tab is playing music.

On a side-note, I recall there was some kind of hardware device pairing (maybe Chromecast?) that used data over voice to establish that you are physically near the other device.