Does it make sense for a web-tablet device like this to have a built-in email client?

Wouldn't it be better to use Gmail or Horde or SquirrelMail or Yahoo Mail or corporate web mail?

I don't think this device's limited device memory space should be used for storing a email client and copies of emails, when there are more than adequate web-based email alternatives available.

What do you think?

Some type of email notification application is needed though. Does anyone know if this exists?

The only issue I would see with using web-based email alone would be the loss of the ability to read your mail while offline where wifi access is nowhere to be found (such as a plane). True about the memory though, maybe it would have been better if Nokia added more memory to the device for handling such space/memory hungry apps as the mail and web browser.

you can also use mail app to alert of new messages.

have you tried the alerting with an open umts or gprs connection?

Using imap with the mail client is faster than using any webmail. Still you can read the headers offline or some important mail you want to have offline.

I'd go with standalone imap-client. Usually you can configure the client to cache message-bodies, but leave attachments or messages bigger than n kilobytes on server. And you can have local folders, where you can drop important messages to which you want to reply when in plane etc. I use imap whenever possible. That way you can have multiple clients, use webmail and have messages in one place (the mail server). Easier to backup, move to new client, have shared folders with others.