Oh right... because putting your critical secret information into a huge, buggy, extensible, unaudited, complex, and constantly changing operating system is so much better!
Or, from another point of view, an attacker has to bypass Linux and OpenSSH security in one case or bypass Linux, OpenSSH and Chrome security mechanisms in the other case..
I understand what you mean, but I'm saying that compromising the sandbox can be looked as well as an additional step to achieve.
And more so if, for example, address space randomization is offered by the OS. In this case the security model is reinforced, rather than weakened.
but I'm saying that compromising the sandbox can be looked as well as an additional step to achieve
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.
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.