There’s not much work on a pure Servo browser beyond experiment. They’ve just various uplifted Servo bits like webrenderer and stylo into Gecko.

There's this which I'm hopeful for: Android Components [1]. If Mozilla make it easy for Android apps to use Servo as the shell for modern web apps, then the improved performance might make it worth it to "restrict" yourself to using only the features supported by Servo (i.e. without many of the workarounds that make old websites work).

[1] https://github.com/mozilla-mobile/android-components/