For most people, sure the odometer will be fine, but some of us live in rural communities and have vehicles that are used a significant amount of time off public roads, but still need to be taxed for their on-road usage - think tractors or road-legal quad bikes, for a couple of very obvious examples. A simple "per mile driven" based on the odometer is not the perfectly fair "one size fits all" solution that it might at first seem to be if those kinds of vehicles go electric at some point, so I think a little more nuance may be required before this scheme sees the light of day. Privacy concerns aside, many of those issues could easily be addressed via GPS-based tracking of just public road usage, and could also enable more nuanced billing to try deter drivers from using busy roads at peak times, effectively turning any road that is applied to into a toll road.
It should also be noted that this is on top of existing vehicle tax, which is paid as an annual fee in the UK. People with large SUVs and commercial vehicles will still be paying more to drive those vehicles per year, but whether the plan is to shift more of that tax to the per-mile rax rates based on criteria such as the likely amount of road surface wear they will create, e.g. different per mile rates for larger vehicles, isn't yet clear, either. Overall, it's probably the fairest system for users of different types of vehicle classes and power trains to pay their share of the public highway costs, but the devil is always in the details and at this point there are scant few of those available to see where the issues people ought to be concerned about might lie.