If Google can't read your email anymore
Will they see to it that the plugin has a fall down the stairs maybe?
Mozilla might even have a jump on this. The Firefox Sync system already offers the means to authenticate and download private data to a public machine, and the encryption is implemented in JS client-side. It could conceivably be used as a way of accessing your private GPG keys securely when on the road too, as long as nothing was cached unsafely. Just a thought...
While Gmail is all HTTPS, and plugins (can) allow relatively sandboxed execution environments, the browser as we know it is simply not the place to handle cryptography. Attack vectors are simply too numerous.
When I refer to the browser 'as we know it', I'm specifically referring to something which silently and continuously auto-updates, changing its code routinely, and bringing out glitzy interesting features as a priority over solid, safe implementations. I don't know exactly how Chrome's plugin sandboxing works now, but even if I did I wouldn't in a month's time.
This product brings in some crucial safety belts not addressed specifically in the article below, but it's a good indication of why most people should be suspicious of front-end based security methods:
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