So I'm just thinking about how this would work, in a perfectly non-competitive world:

There'd need to be some Browser Standards Association to implement and suggest browsers to add to a list of "certified browsers", with transparent requirements to be included to ensure low quality or outdated browsers aren't included. The OS would need to implement that entire list in a randomized format. There'd preferably be some sort of built-in pros/cons list of the browser, I suppose these could be put together by a combination of the BSA and the competing browsers.
But these pros/cons won't be understandable or significant to 95% of people.

The BSA would also want to ensure there's diversity not just in browser and companies (like Opera getting 3 fucking entries), but would also want to ensure there's a variety of browser engines (preferably not just chromium and webkit).