TL;DR: It should be, and likely will be soon
Throughout the history of the internet and browsers, many well-intended features have fallen prey to abuse: popup windows, alerts before closing a page, back-button redirects, mislabeled links, download buttons, etc. Audio is no exception, with auto-playing videos and advertising becoming more common in recent years.
The line between usability and safety
The problem is, audio is the second most used sense when browsing (naturally behind visuals). Almost all video content and especially all music/podcast content we consume requires audio. Disabling this by default or even asking for permission creates the possibility of confusion.
Consider this scenario: a user visits a news website with an auto-playing video ad. They decide to deny audio permission to that website. A few months later, they are reading an article on that site with an embedded YouTube video with some news footage. They click play expecting to hear the audio, but it is disabled. Unless they remember disabling audio for that site and understand how to re-enable the audio permission, they are not hearing that video. Expecting sound and not hearing it is incredibly frustrating, not just for browsers. Users must be made clear of when to disable audio, and how to re-enable it if needed.
Workarounds
Modern browsers today have implemented workarounds to address audio abuse:
- Chrome and Safari display a sound icon for tabs that are playing audio
- Chrome (and maybe others) allow users to mute a tab
Future Solutions
Google is experimenting with this very permission (Source: Android Police).
According to Google's François Beaufort, the Chrome team is still experimenting with this feature. In the early version, the sound toggle is in the page info popup, which you can access by clicking on the far left of the address bar.
Like so:
Safari 11 will block auto-play videos (Source: AdAge).
Safari web browser will now feature the ability to keep websites from automatically playing video whether or not consumers want it.
I'd look to mobile for another example solution, where most apps don't play sound until the media (video, audio) is tapped on. This could be worked into browsers as well, where a user has to mouse over the content to hear it.