Mozilla thunderbird as a website would be more conveinent at times then starting an app or leaving it on idle so that is uses up your resources in the background.
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I think a better idea would be a lighter version of Thunderbird as a Browser Extension.
You know, so you can easily open links in the browser or drag/drop links into Emails or Feeds. Maybe even sync feeds across devices.
Normally i am all for adding extension, but a whole Mail Transfer Agent as an extension ... might not be a such a good idea.
One Reason being that SMTP/POP3/IMAP ... are completely differnet protocols from HTTP/S ... it might not be the best idea to add this bunch of complexity even as an extension.
Also the current Extension API is to limited to even provide this functionality.
The minimal requirment would be to allow extensions to establish TCP connections, which AFAIK, is not comming any time soon (if at all), - since this functionality might be powerful but can also be misused in quite a few ways.
So having a dedicated application just for email messaging might not be the worst decision (fow now)
Utilizing web apps will revive the Mozilla Suite in a practical way.
I just posted a new idea on this topic but just adding my support to the thunderbird web-app concept here too.