So you don't want Firefox to be able to read SSH keys. Privilege separation and sandboxing is the correct solution to this problem. Full disk encryption will protect the data at rest.
I think firefox should be able to access SSH keys as should any other application, but I should be notified when this is going to happen. From there I should be able to trust an application indefinitely so long as it's executable doesn't change (i.e. maintain shasum hashes of any trusted executable and make sure that if the shasum changes, you are informed that it has changed. e.g. "The executable Foo has changed since you last trusted it, would you like to trust it again?"
Privilege separation and sandboxing is the correct solution, but there is no reason that these cannot be improved upon to make this more friendly but still secure. Accepting the status quo solutions is akin to accepting that it will always remain a niche solution that never gains acceptance and traction in other areas of our lives where we want security and a solution that is inherently decentralized.
I'm actually really tempted to do that now...