Road tax has nothing to do with a vehicle being able to use a road. The sole purpose of road tax is to tax vehicles on the emissions which their vehicle sputters out. Efficient cars don't pay tax as they are efficient, and electric vehicles don't. As a scooter is an electric vehicle, road tax should not actually be a factor.
With regards to pavements/main roads, you could say this for bikes as well. It is illegal to cycle a bike on the pavement, but you don't need a licence to cycle one on the road. This is just as dangerous as a mobility scooter as a lot of cyclists come onto the road and don't have a driving licence therefore don't know how they work.
My opinion, mobility scooters should be used on pavements, the people who use these need to get into shops, post offices...
Bikes, if you are on the road you should have a test to say you can cycle on these roads safely. At the end of the day if a cyclist does something wrong, it is the driver that mainly gets the blame and has to live with the guilt of injuring someone, when it may not have been their fault. Any other time you should be on the cycle path. Most cities have a number of cycle paths where you can quite easily get from one part of a city to another.