I’d say that simply hiding them when clicked would cause more problems than it solves since these links are a very convenient way of getting to currently relevant posts (to mention just one use case: you have a number of notifications about replies and might first read all of them before deciding which ones to the reply to).
That said, I agree that it would be nice to be able to dismiss selected (rather than all) notifications in order to get rid of unwanted clutter, especially various badges or posts that you do not want to react to. Perhaps every notification could have a little X in the top right corner which will delete/hide the notification from the user menu (not sure if this should also apply to the notification page).
If this would work even when the notification has not been clicked, this would also be a solution for a nuisance that was discussed earlier (can’t find the topic any more), namely that people would like be able to mark like or badge notifications as read without actually visiting the link.strong text