I haven't seen any work estimating this. I have as part of my work spent some time trying to estimate the upstream effects of private cars (and other forms of transport) and it quite quickly gets very hard to find very much data. Even something quite basic like road maintainance gets quite difficult to unpick. So we know broad generalisations like heavier vehicles cause more damage but its quite hard to isolate this connection with individual traffic make ups (e.g. how much change in costs does a 10% change in average vehicle weight cause)
Sadly, we don't have a culture that particularly wants to know or track the costs. I'm not sure I'd be so confident though that the administration costs would be completely neglible. Some of the costs are quite high level: highway engineering, infrastructure and enforcement which can have high labour and materials costs. Probably what you need is a "natural experiment". Find a town or city that already happens to have a strange policy (I vagually recall somewhere that has a network of golf cart usage?) and try and ask the relevant authority whether they can provide the back history of spending and compare it to a similar size "normal" road network.
Related bugbare of my mine is the term cycling or walking infrastructure when in reality most if it is actually only necessary because of cars so its really car infrastructure (i.e. to facilitate cars going non human speeds without killing people or damaging buildings).