You don't really believe that, do you?
What do you think would happen to property values in and around Dublin airport if the airport had to be relocated for some reason? Would the loss of local jobs have zero effect on local property prices?
Of course publicly funded amenities impact private property values!
A house in East Wall may well be cheaper than a house of a similar size and specification in Clontarf (which I would suggest has better publicly funded amenities) but it would still be a heck of a lot more expensive that a similar house in the wilds of Donegal.
Dublin property prices were higher than Donegal prices before the airport was even dreamt of, they would be even if the airport was re-located.
Dublin airport was put where it was because the people were there.
A house in the capital city of the country, all other things being equal, will be a lot more expensive than a house in a remote rural location. It's where the people are. It's where the jobs are. The government doesn't subsidise Dublin's popular music venues, shops, pubs, restaurants, cinemas etc in fact they tax them heavily. They all make Dublin a more attractive place to be.
The Three Arena receives no public funds, Dublin's museums receive millions.
Can anyone say one or the other has a bigger impact on Dublin property prices?
There are properties in remote locations which have had huge public funds expended on them for reasons of flood protection, or transport subsidy of helicopters, ferries or planes for islands. If property tax should somehow be linked to the public funds that have gone into the area their property tax should be about 1000 times higher than it is. Maybe it should be and they should be paying for all those services from their own LPT, regardless of the value of their houses, they should pay their own way.
The level of funds per person in the area spent on Knock airport is massive compared to Dublin airport (and its commuter belt). On that basis, we should expect houses in Knock to be more expensive than Dublin, they're not.
Houses immediately around Croke Park would be more expensive, not less, if they weren't invaded every summer weekend for GAA matches.
The relationship between public funds and private property prices can be negative and positive, even if all areas received the same public funds Dublin property prices would be higher than everywhere else, I don't see any basis for using the distribution of public funds as the basis for justification for property taxes, its effect is way too haphazard -rather, it should at the very least be about paying for local services.
You'll have to convince me on the basis of the "productive enterprises" argument.