Re: If you buy a new car, you have to tax it even if it already is taxed by the previous owner.
"The ANPR camera would have to check three things, now they only have to check for tax."
Sorry but you are wrong. It is no real effort for an electronic system to check three things, but also it is possible to tax a car with 1 month MOT remaining and 1 month Insurance (or cancel the insurance after a month, or stop paying it).
The ANPR still has to check all three things (and still does) so there is no longer any sensible requirement for tying the Tax into having an MOT or Insurance. The tax should be able to be purchase for the car in question by anyone (not just the registered keeper) and start on the day you purchase it and end exactly 1 year later (for 12 month tax) rather than at the beginning and end of whole calendar months. No requirement for the V5C and no waiting for the MID to update.
Insurance managers to insure from an exact time on an exact day.