Oh right... because putting your critical secret information into a huge, buggy, extensible, unaudited, complex, and constantly changing operating system is so much better!
When running OpenSSH inside Chrome on top of Linux you will be affected by any security bug in Linux, OpenSSH or Chrome.
It's not that hard to understand, really.
It's an oversimplification
When you load your SSH-Keys into Chrome and the Chrome sandbox is compromised then there is no further layer between the attacker and your keys.
This is a new attack vector in addition to those that may exist in SSH itself and your operating system.
You're making no sense. The previous attack vectors don't go away when you put your keys into Chrome. Chrome becomes an additional option for the attacker, not an additional "step".
A house with two doors is less secure than the same house with one door.
Yes, you can use ssh-agent with chrome (if they have that implemented, I don't know). Yet you are still in trouble when the chrome sandbox gets compromised, because all your keystrokes are passing through it.
If the sandbox is compromised to have file system access, a process can read your keys from ~/.ssh as well as chrome storage files. Otherwise a webpage has to escape its own sandbox, bypass the native client's sandbox (in a different process) composed of the inner and outer sandbox and then access the native client.
I'm not saying that it's impossible, I'm saying that using a simple analogy as "a house with two doors" might not be the best.
Or there could be just some really dumb bug that somehow enables cross-process access. With javascript. You know, one of these silly brown-paper-bag bugs that are not supposed to happen.
Either way, this is the second door. It may be a shiny steel door, but it's an additional door.