In other words, make it more declarative and less verbose.
The browser could always increase the apparent audio latency by buffering, but that reduces the ability of music apps to perform well.
Move responsibility for the syncing to the browser and then the app doesn't need to know anything. In short, I can put it together and send it to you, or I can send you the bits and tell you how they should be put together.
A graphics frame appears on the screen at a specific time. (For VR, it is a definite time, and this is critical. For normal video or games, a little bit of slop, maybe a few ms, is probably okay.)
For audio, humans are sensitive to 10 ms deviations or even less.
Any API that works decently will need to synchronize audio and video, so there needs to be a way for a program to say “this audio sample should play are the same time as this video frame is shown”. But an API should also allow programs to react as quickly as possible to user input. And Bluetooth headphones, in particular, have very, very high latency.
So designing an API that performs well without revealing the latency is hard.
I do think it would be good to cleanly separate normal web pages and games, though. For pure content, none of this matters except that video needs to maintain synchronization. But normal content does not need clicks to translate quickly to video changes.
The browser is the presentation layer, it needs to know the latency of your headphones (or the system does). Why does the content provider need it? What's wrong with "here is frame A, please play audio A at the same time (while taking into account the latency that only you know about)" as a request?
That's ok. Then I have the option to weigh whether the risk is worth it or rather not. 9 out of 10 times it is not, in rare cases I will allow the js to execute.
How do you explain to one of these "I'm not good with computers haha" types what a CDN is and why Taboola CDN shouldn't be allowed but Akamai should be otherwise things Won't Work Right. Even if they're capable of learning [1] why should they care, when all these security measures actively make their life harder?
Blocking audio and other fingerprintable surfaces by default, with a "click here to enable audio / video" and a "remember my choice on this site in future" is the only way it can possibly work, because 99% of users will only ever go for the laziest option. We need to have protections for them that work regardless of (or in spite of) their skill level.
As a major side benefit, websites will stop randomly playing audio without permission.