Feature suggestion: Monitoring of 'unseen' tweets done on Twitter server, rather than locally in a Twitter client like Twhirl

There is a really great feature in Twhirl that displays a small yellow star at the top right of all new and 'unseen' tweets - which I'll call the tweet's 'unseen status'.

I think it would be really great if the Twitter servers would monitor each tweet's 'unseen status', rather than it being done on the local machine, via a Twitter client like Twhirl.

(The guys at Twhirl sensibly pointed out that this 'unseen status' feature needs to be in Twitter before they can add it to Twhirl)

This feature would help tremendously when going from one machine to another (from work to home for instance) - when both machines have Twhirl logged into the same Twitter account.

The Twitter client could update the Twitter software (on the server), on which tweets had been 'seen' locally - and this could be done at the same time that the normal network-API-requests/auto-refreshes happen.

I've included two images to illustrate what I mean by this 'seen' flag...

This 1st image shows when a single tweet is cliked, and therefore marked as 'seen':



This 2nd image shows the button that marks all tweets as 'seen':