In a single capital market with a single currency, is there any reason why a company located in Ireland should float on the Irish Stock Exchange in preference to any other exchange? What the company wants is to raise capital; there is no reason why it should have any particular preference for Irish capital.
The customers of a stock exchange are not really the companies that float on it, but the investors that trade on it. But in an era of global capital markets and instant communication investors care less and less about where a stock exchange is located. I think smaller exchanges survive by developing specialisms and niches, not by appealing to local companies to list there, and local investors to trade there because, really, I don't think there is no compelling reason for local companies or local investors to do that.
The Irish Stock Exchange has had a tenuous existence for some time. Originally the Dublin Stock Exchange, it became the Irish Stock Exchange when separate exchanges in Cork and Belfast were folded into it — a harbinger of things to come, perhaps. In 1973 it ceased to be an independent exchange itself, when it became a division of the London Stock Exchange, which rebranded as the International Stock Exchange of Great Britain and Ireland (which also incorporated the Scottish Stock Exhange and a number of regional English exchanges).
That merger was reversed in 1995 and it became independent again, but in 2014 it was taken over for a second time, becoming a subsidiary of Euronext and being rebranded as Euronext Dublin. Euronext also operates exchanges in Paris, Amsterdam, Milan, Lisbon, Brussels and Oslo.
Within this context, Dublin as a centre for trading shares doesn't make a lot of sense. There's still an equities market operated out of Dublin but it's not expected to grow because, really, why would it? Euronext Dublin increasingly focusses on debt securities and funds, and this is where it's future likely lies. The parent company, Euronext, offers markets in almost everything — equities of various classes, bonds and debt securities, commodities, funds. Within this framework its Dublin unit is well-positioned focussing on funds, since Euronext is the biggest centre for debt and fund listings in the world.
Tl;dr; the equities market operated by Euronext Dublin is not a big source of funds for smaller Irish enterprises looked to grow. It probably doesn't make a lot of sense that it would be. Whatever measures might be adopted to improve access to capital for Irish SMEs, Euronext Dublin is probably not likely to feature in them.