We actually just received a request this week for this option. But sorry Steve I'll have to disagree with your definition of an Incident/Problem. Anything that is 'broken', 'faulty', etc. will be an Incident. A fault with a high use application will cause numerous calls into a helpdesk/service desk. So we are talking about a high number of singular events. A 'master' Incident is normally used for these situations with subsequent customer calls added as 'Impacted' onto the master Incident. That master Incident is then resolved when it is either fixed or a workaround is in place. After that point a Problem record can be opened. Problem records are used to find the root cause of Incidents and are normally opened when you ask the question 'so what actually caused that issue' and the answer is 'we don't know'. Once the Root Cause is determined then it becomes a Known Error, which can be either used to fix incidents or workaround them. Finances normally come into force on some Known Errors, easier to reboot a server once a week then to replace costly main circuit boards or upgrade software taking hundreds of hours.
So to go back to the original question here, yes having the means for customers to 'Impact' themselves onto a master Incident would be of great benefit as that then can show the true impact of the Incident on the organisation.