Miles seems like it might not be worth the added cost of administration. Also note that road damage as a function of weight goes up by roughly a power of 4. Doubling a vehicle's axel load causes 16x the road stress, though that may be in line with what you were suggesting and may even add weight to your point.
state inspections here record mileage and is used to validate low mileage discount on insurance. it could also be used to determine road use tax. as for public vrs private roads. assume all travel is public roads and let the user provide acceptable documentation that they traveled on private roads (gps tracks)