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Have you heard of Ševčenko's law? One hundred and fifty years, or more, of ""serious"" history and good old Dan's dog is the first to pick this tree. 
From what I understood of it, and it's rather over my head, Mc Carthy has a point. However, it would be throwing the baby out with the bathwater to adopt his dates before anyone else does. It means that every date in a book needs to be Mc Carthy-ised. 
And even then I have very serious doubts about the accuracy of the results. Mc Carthy's method may give accurate AD dates, but I suspect there are problems. Take 763. He's content to put Domnall Midi's death in that year, just as the historians are, but why does AD 763 start with an event dated to 20 November? Fair enough, that could just be a glitch from the compilation, but it could also be that whatever the source was, its years did not start on 1 January or March 25 but instead on 1 September. Adding that to an article would be WP:OR, so we won't do that - we do when it's Bede's years because people have discussed it in print, but this they haven't - but we can take it into consideration here when deciding what to do. 
The Chronicle of Ireland was compiled from lots of sources and it would be a reasonable bet that even if most or nearly all of them started the year on 1 January, some would have done so on 25 December, some on 1 September, and some on 25 March. Even if Mc Carthy's system is perfect, you can only be entirely confident about the year if the event falls between 25 March and 31 August.
If we can date events to within a year either way, that's good, if we can date events in the 7th century to within 2 or 3 years, that's marvellous. If it were me, I'd go with ""historian"" dates, i.e. what Byrne, Charles-Edwards and the rest say, and add Mc Carthy's corrections in a footnote, which is what is done with Penda of Mercia and other C7th Anglo-Saxons where there is a similar, but smaller, problem. We can ask for outside opinions, people like   (Talk) "