Most web apps are unlikely to need high-precision timers. For games, however, Date.now() offers only millisecond resolution, which can make it occasionally inadequate.

I'm developing a website that will require somewhat high frequency timing to account for network latency but I think standard getTime is accurate enough with millisecond accuracy which I think will satisfy my requirements (I still need to test this though).

I can't think of something that needs microsecond level timing though.

A browser based DAW/soft-synth?

That's one of those things that seems better suited to being a native App.

I realize there's a whole group of people who want to make the web browser as powerful as native Apps but I for one do not.

I agree; I would like to see a move away from trying to cram everything into a browser app, and towards adding better connectivity and community features to native apps.