That's a single report issued for "Clean Air Day". It's interesting but I'm not sure how independent it is. It also applies to the UK rather than this country.
But let's assume it's equally valid here.
From the first paragraph, health-related costs "of an average car in inner London over the vehicle’s lifetime was nearly £8,000". That works out about €740 per year
if we assume the car's life to be 12 years.
The 2018 Irish budget for road improvement/maintenance is €909m. With 2.5m vehicles on the road, that works out at €363 each.
so let's say that adds up to cost to the state of about €1.1k per car.
On the other side of the equation... let's look at a 1.8L Toyota Avensis.
Purchase cost is about €30k. VAT & VRT work out to be €12600. Again assuming spread over a 12-year life, that's €1050 per year
An average car drives 16000 km per year (more for a diesel car, but let's stay conservative). At 12km per litre, that works out to be 1333l per year. With 60% of that being tax, this motorist pays €1144 fuel taxes per year
Motor tax for this car would be €280 per year
. (there are cars paying less, but there are also cars paying the 2008 rates which are far higher).
Insurance Levy is €25 per year
With whats above, I work out cost to the state per car to be about €1000 per year, and the state takes about €2500 from the motorist in motoring-related taxes/charges per year.
I'm not sure if I've missed other significant taxes - I haven't included on-street Parking costs, tolls, VAT on servicing or on NCT. These are trickier to estimate, and I'm not too bothered.
If we want to be difficult, we can add nebulous things to either side of the equation. The anti-car person could talk about costs due to traffic congestion, the pro-car person could talk about the benefit to businesses of having people able to drive to shopping centres. But I'm just focusing on measurable things.
I think it's fair to say the state "taxes the arse off" the motorist.