>The browser remembers my choice for each site, how many new, different sites do most users visit per day (that would need audio)?
How many sites need notifications? And why do I need to decline that permission at least once a day if not more often?
And the issue is that putting this behind a notification removes the downsides of asking for it. Currently if you play audio un-prompted you piss off (a percentage of) your users. If that was behind a notification, you would only inconvenience those users, so there's less of a downside of trying it assuming that only people that want it would click "yes".
My "perfect solution" would be for the major browser developers to get together, and come up with a web standard for where these notifications/prompts will live in the browser chrome, and roughly what they will look like, so that everyone can standardize on a similar UI. Then move from a prompt to a "badge" of sorts, and give websites the power to instruct users how to discover and switch that permission on/off when needed.
I believe on desktop chrome most permission prompts live in the upper-right corner of the address bar, if we could all standardize on somethign like that (at least on desktop, then figure something out for mobile) website owners could then instruct users "to see notifications, click the (standard-notification-icon) up there and select 'yes'".
For "rare" things like notifications, camera access, gps location, and others that seems like a good tradeoff to me, but for "more common" things like audio/video, I don't think it fits.