And browser development is exactly not the area where I would like to see the "move fast, break things" attitude. While firebase may be sloppy with security and thus unfit for certain purposes, I would expect competent developers of a browser to do due diligence before considering to use it, or whatever else, for anything even remotely related to security. Or, if they want to experiment, I'd rather that be opt-in, and come with a big banner: "This is experimental software. DO NOT attempt to access your bank account, or your real email account, or your social media accounts".
With that, I don't see much exploit potential in learning stats like the number of cores on your machine. Maybe slightly more chances of fingerprinting, but nothing comparable to the leak through improper usage of firebase.