Yes, but not a very good one. And you get more or less the same ban for three minor speeding offences as you do for killing someone....
Except that totting-up isn't the only way to attract a driving ban: the more serious offences almost all carry the possibility of a much lengthier ban and the requirement to pass an extended driving test before being able to apply for a new licence. http://www.legislation.gov.uk/ukpga/1988/53/schedule/2
Totting-up is a practical way of trying to ensure that an offender's previous summary convictions are taken into account. With more serious offences, criminal convictions are recorded with fingerprints for identification and the court can ask for social inquiry reports before sentencing. Indeed, they normally must obtain reports before sentencing somebody to prison.
I'd agree that there should be more attention paid to somebody's psychological state, especially in road-rage cases, and I've posted more than once that being technically proficient behind the wheel doesn't necessarily mean somebody will be a good driver.
One elephant-in-the-room is that without detection, sentencing policy is academic.