VRT is paid whether you buy a new vehicle from a manufacturer in Ireland or elsewhere in the EU. It's also paid if you buy a new vehicle from outside the EU, but in that case there will additionally be import taxes.

It might be that the administration is different (e.g. the large vehicle importer usually pays it, but you pay it yourself if you're buying some exotic Lotus direct from Britain).

It is a completely different purpose.

Denmark has high taxes for registering a vehicle for public use to pay for road construction or maintenance and to discourage car use (or rather, to make the people using the roads pay their way).

The EU has import taxes on vehicles to protect its own vehicle industry, to both maintain that industry and the jobs within it.