Can I phrase the same objection in a more HN-y manner?
SSH terminals are high-sensitivity software. We frequently use them, with very sensitive credentials, to log into secured servers. There are two zones of trust involved: we trust that our local machine is not rooted, and we trust that the server is not rooted. The magic of SSL means that no matter how foul everything is between those two zones of trust, we can't get compromised.
If we embed the SSH terminal in the browser, we now have four zones of trust: our local machine, the browser, the SSH terminal extension, and the server we connect to.
This is a very scary broadening of our attack surface. While the terminal app siting on your machine is decades old and has been tested extensively, the browser extension almost certainly has not. The browser extension, in addition to possibly having vulnerabilities itself, is executing in the context of the browser. The browser is a very scary place to be, because its whole mission in life is connecting to the untrusted, infected cesspool of the Internet and then doing what the Internet tells it to. By grace of God and Google engineers, we generally assume that our browsers aren't going to crack out of the sandbox surrounding the sandbox surrounding the sandbox that all that evil Internet stuff is executing in, but we expect that, in the normal course of operation, those inner sandboxes are going to fall into the hands of the enemy, repeatedly.
It therefore seems to be an exceptionally bad idea to take our holiest-of-holy credentials and move them inside the sandbox, closer to the attackers.
This is particularly true in terms of a risk/benefit analysis, since the risks are incredible and the only benefit is "Saves you from having to do a single key chord to pop open an additional terminal on your machine."
This is moot if you have total confidence in the Chrome and Native Client teams to never have a mistake which lets someone, e.g., read arbitrary process memory. That's happened before -- Mark Dowd et al found it. That would be pretty sucky if it happened on a browser you logged into your bank, because the attacker can probably grab your cookie and banking session. It would be much worse, though, if it happened on a machine used by a bank sysadmin who unwisely decided to use a terminal within his browser, because why steal one session when you can just steal the bank? (n.b. Note how this is possible without causing Chrome to execute arbitrary code or defeating the OS's protections against Chrome doing stuff outside the Chrome-box.)