A. (30 seconds of googling.) "Your mailbox is full because your quota looks to
be about 1/100 what modern email systems typically provide. You need to
switch to a provider with reasonable quotas."
If they are unwilling to switch providers, there is also the option
(if using POP) of checking more often since (unless you say Leave on
Server) that will clean out the Server Mailbox as you download.
For the large fraction (probably a majority now) of people who read
their mail on their phones, the only option is IMAP and there is
nowhere but the server to keep the mail. For reasons already
discussed people don't want to abandon an address that all their
friends have in their address books, so they resort to painful kludges
like setting up another "secret" address at a provider with a giant
quota and forwarding the mail there that they want to keep.
Ned's point remains that the pain of switching addresses is
substantial, expecting everyone to get their own vanity domain is
absurd, so there is and will continue to be considerable friction
even for lousy mail providers.
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