In the Irish case, I think it has to do with the translation of a formerly oral vernacular tradition into a literary one. Ireland was particularly unique in Western Europe in that it had never been incorporated into the Roman Empire and consequently retained most of its socio-political structures after the conversion to Christianity. One of these surviving elements was a large class of hereditary educated specialists called the áes dána, the 'men of arts' which included poets, lawyers, judges, doctors, satirists, genealogists, bards and historians whose duty was to either enhance the honour of their noble patrons or to aid them in the everyday functioning of a noble estate as a sort of 'Mandarin class'. These men (and sometimes women; some legal texts mention female poets and satirists) would have benefited immensely from the introduction of the written word that came hand-in-hand with Christianity.

This was especially true of the Irish lawyers and judges who were educated entirely in the vernacular and were required to orally memorize vast swaths of legal theory and case precedents before the introduction of Latin script. It's no surprise that the first legal texts began to be produced relatively shortly after the island's conversion to Christianity (in fact all Irish legal tracts were produced in Old Irish, between 600 and 900 AD) and were subsequently glossed over by legal students and commentators. The Senchas Már is an example of such a text, which was glossed over numerous times in the centuries after its production. Interestingly, Old Irish was the first non-Classical European language to develop its own dictionary, sometime in the late 9th century.

Vernacular poetry and satire were also very important in early Irish society and likely benefited from the introduction of literacy as well. Ireland was an honour-bound society and poetry could be composed to enhance a patron's honour, or a satire could be composed to efface a rival's honour - satire was actually feared as a semi-magical weapon that could bring about a literal loss of face if left unchallenged, whereupon the victim of a satirist might lose their legal and social status that depended almost entirely on their honour. Besides these more spontaneous compositions, many traditional myths and origin legends of the Irish and the various dynasties that sprouted up about the island around this time were also composed and written down for posterity, or new genealogies were invented to tie conquerors to their newly conquered subjects.

So the vernacular written word thrived in early medieval Ireland, likely because there had already existed a large caste of educated, non-clerical professionals who received their entire education in Old Irish. The introduction of the written word allowed these professionals to codify the knowledge that they had traditionally passed down orally and most importantly, to immortalize their patrons' deeds and honour in ink.