One reason for not making such payments dependent on the local cost of living, is that you may otherwise be officially in one country, while really living elsewhere. If the EU wide basic income isn't enough to live in Dublin, the Irish gov't still could provide additional welfare programs for people living in Dublin, or keeping the kind framework they have now for dealing with such problems.
In the worst case, it is in Ireland as if the EU wide basic income doesn't exist (if its too low to matter in Ireland at all).
That wouldn't diminish the possibility to use it as a transparent mean of solidarity within the EU or for EU wide taxes in environmentally damaging substances.

Der Amerikaner ist die Orchidee unter den Menschen
Volker Pispers