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If my account is deleted by the ISP, then those e-mails are lost.
Of course. But you (and I) would still have all of our previous emails because we download them to
our computer. I can only imagine that someone who never can or does download their email is using the 'service' purely for enjoyment/entertainment. I can't fathom any business not having physical possession of the companies/employees messages. Nor would I want to lose, because of some snafu at the ISP even the messages from my Grandkids. Furthermore, I often register at some sites that send a 'starter' password via email. And then there are the ones you may get when you forget one. Either way, I wouldn't trust any ISP to store that kind of info about me, I want that off their servers ASAP. As long as it's out there, it's searchable, accessible and insecure as far as I'm concerned. And "insecure" doesn't have to mean that a hacker can get, either. The whole point of this thread is that a major ISP trashed a lot of peoples messages, just hope most had downloaded the majority of them before hand. Of course, if an ISPs servers are hacked, any and all data could be available, but there's no use in tempting fate by leaving all my stuff on the table.
The only reason I could justify a non-downloadable email account would be if they also provided me with unlimited aliases or mailboxes, throwaway accounts, in other words.
Leaving messages on some server is only marginally better than putting your personal info on something like Facebook (or even at TS!), IMHO. You have no idea who and when some other party might find or use your info. Just doesn't seem wise to me. Of course, I'm paranoid, like that!