Unfortunately they are designed to be used by just the sort of people who may have difficulty passing tests - would you be happy to take away someones only means of getting around not because they had ever done anything dangerous but simply because they could not pass a formal test?
There are an estimated 300,000 or so mobility scooters in the UK - accidents do occur, but is the risk of accidents going to be sufficiently mitigated by introducing a test... we still have car accidents and everyone has had formal training so we could never expect to bring the mobility scooter accident figure down to zero. I don't know where it stands at the moment but I would wager that rate of occurrence of serious accidents is vanishingly small compared with the number of journeys made on these devices.
The speed limit on the pavement is 4mph by the way - the 8mph limit if for the road legal class of scooter. See the rules governing the scooters here:
https://www.gov.uk/mobility-scooters-and-powered-wheelchairs-rules/overview