I suppose the short version is that because, by the time of independence, English was the primary spoken language.

Irish was in decline in the 19th century, in terms of speakers. Some scholars regard it as a minority language by that point, while others see the Famine as the major turning point. The oft-cited 1841 census Ireland recorded over 8 million inhabitants, with only 4 million of those being Irish speakers, and by the 1851 census (post-famine) only 23% of the population reported that they could speak Irish.

The reasons for the decline of the language are still discussed in scholarship to this day, one of the reasons usually given is that when the National Schools were established in the 1830's, Irish was not included in the curriculum and the medium of education was English. This, of course, doesn't account for only half of the population speaking Irish by 1841, and I personally think we can't underestimate the effect of English being considered a "prestige" language: after all, the result of English colonisation was that the majority of wealthy landowners were English, or even English speaking. Irish had increasingly become less "advantageous" than English and I don't think we should be surprised that parents were encouraging of children learning English, and discouraging their children from speaking Irish. Especially after the Famine, there was a cultural perception that Irish was associated with poverty, as it was the rural (and often Irish-speaking) poor who were affected the most by the Famine. Another famous example is that of the Maamtrasna murders, in which three Irish speakers were wrongfully convicted for murder because they spoke no English, the courts functioned through English and they were not given a bilingual lawyer. Irish was marginalised, and it wasn't seen as beneficial to be used, and potentially dangerous.

So, by the time we reach the creation of the Constitution, we have the majority of the population as English speakers, and not all of the Republican leaders were Irish-speakers. There was initial enthusiasm for implementing for Irish infrastructure, but with the outbreak of civil war and the fact that it would involve forcing the majority of the population to learn a second language, I don't think we can be too surprised that the politicians opted to run things through English.

I have a bit of a hodge-podge of sources, as off the top of my head I can't think of anything that discusses this single question in particular depth, but the history of Irish has a lot of really great sources.

Articles such as Antain Mac Lochlann's "The Famine in Gaelic Tradition;" Erick Falc’Her-Poyroux's "The Great Famine in Ireland: a Linguistic and Cultural Disruption;" Séamus Ó Buchalla's "Educational Policy and the Role of the Irish Language from 1831 to 1981" are all great.

In terms of books obviously Pádraig O Fiannachta's Milis an Teanga but that's clearly not accessible to English speakers. I believe John O'Beirne Ranelagh's A Short History of Ireland gets into it some.

As for Maamtrasna, Margaret Kelleher's The Maamtrasna Murders: Language, Life and Death in Nineteenth-Century Ireland is pretty good.