If they do, they will be replaced, just like iexplore was. So they won't stagnate unless they are stupid and want Firefox to take over.
From a practical perspective, ten years of stagnation is not very different from indefinite stagnation. Even if there's a light at the end of the tunnel, we're going to have to spend a huge chunk of our lives suffering through it.
And with Google, stagnation is probably the best case. If they continue to "move things forward" as a browser monopoly, they'll probably force many user-hostile things (like their recent proposal to cripple ad blockers https://bugs.chromium.org/p/chromium/issues/detail?id=896897...).
That's just my idea, though. Hopefully, the current sad state of the web and the coming browser monoculture will spur others to experiment too. I know some gaming companies have experimented with the distributing and executing of x64 binary executables using the browser. I know others are looking into ways to chop up and do progressive loading on binary executables.