Gmail can do this too, right? Or are their target consumers not supposed to know about web mail? I think you can even send from the non-Gmail SMTP address.
This service was started at a time when GMail, (and a lot of web-based mail), didn't exist and a lot of people used the email address provided by their ISP - many of which didn't provide a web interface to email.
EDIT: The part below is a general reply, not related to the daddydave quote above. (Just thought I'd add that for the sake of clarity.)
Put it this way:
If you need
to access your email and
a) you don't have your 3kg laptop with Thunderbird because it was stolen along with all your carefully downloaded private emails, and
b) you don't have an email service with a web interface, and
c) all you've got is is your portable version of Tor/Firefox on a USB stick and you're at some disreputable internet cafe in Nigeria....
What are you going to do?
It's your choice whether you trust them or not.
I don't have a problem given what they provided me with in the past and the subsequent problems that arose from that use, ie. none.
It was asked whether you would trust that particular
site; for that particular
site, my answer is yes.
If it's that much of a concern whether they have access to your email account; forward it all to another with a different address/password and access that one.