A clear weakness is that mileage readings can be altered. This used to matter on a smaller scale: dodgy second-hand sales, but now more or less anyone could be considered as potentially incentivised to interfere.
The mileage must remain a changeable field since the recording component may need replacement, for example, after accident damage or to correct a fault in the assembly that recording memory is part of.
A more central issue is the synergy between fuel consumption and damage to roads. Heavier vehicles do more damage but also burn more gas and so pay more tax, a synergy between cost and revenue. A flat rate based on mileage alone would equate all EVs as the same regardless of some being massively more damaging than others. We would need different rates for difference classes/weights of vehicles.
There are people who won't care about this but I think that legibility would be a huge concern here. It's one thing to do $X per megameter, but it's another to start breaking it down into various zones etc
At that point might as well just do congestion pricing in cities.
Do it like taxes, have a low rate for the first X kwhs then increase after. Great aunt Mildred gets to heat her home, your neighbour that has a massive house, EVs, jacuzzi etc etc pays more.
EVs are always going to be an outsized user of electricity, and it's unclear to me why someone's jacuzzi should be heated vat free.
I had an actual aunt called Mildred, and she lived in a very old (possibly literally Tudor, not mock, actual) cottage with actual fireplaces and so on.
Her place likely used about 42 MWh/year to heat, though this would be coal and wood not electricity because actual fireplace, compared to my house which is so well insulated that it took a week to notice we'd switched off the heating, in winter, while it was snowing outside.
For 42 MWh/year, you can fully recharge a 100 kWh car battery every day and still have more left over than my house consumes in total.
And with solar power becoming cheaper and more common, it's going to be making less and less sense to disincentivize electricity usage.
If we want to preserve and maintain our roads, we might have to...*shock, horror* increase income taxes on the wealthy!