Would the south even want the place?
So, that one's complex. I mean, for a start, the name isn't "the south" or "Southern Ireland", it's "Ireland" because at the time, nobody felt that the country was being split, so much as there was a temporary territorial incongruity that would later be resolved. "At the time" here refers to a period about a century ago, but at that point it would have been akin to referring to China as "Northern China" when talking about China and Taiwan (I don't recommend that by the way, if you ever find some enemy has given you the opportunity to do so).
But as to reunification, every person who remembers a single united Ireland is now dead from old age. Nobody paying taxes today knows it as anything but a proposal, or some dry text in a history book, and that state of affairs primarily came about because the Good Friday Agreement took all the things like border posts and army bases which were acting like petrol in a house fire and removed them, and over time, things calmed down a notch. Not "calm", by normal measures - NI in the good times was still a place where you could put a foot wrong and not get it back - but businesses could business, and families could family and it was a place to live, not a place to flee from. And the border counties in Ireland felt a large benefit from that too; you don't have to actually stand
in the volcano to get burned after all.
So over the last decade or so, anytime someone surveyed people in Ireland on the question of reunification, one of two things happened - either you didn't specify what the economic cost would be and they said yes, or you did and they said no. I think the majority of people here feel that it's a nice academic idea, but nobody wants to take the economic hit that West Germany took from reunification. Now you add in the DUP to the equation and frankly, we've had enough experience with being a religious theocracy (we're right now just absorbing the latest in about six reports on the works of the religious orders in Ireland and this one accounts for several thousand dead children, the bodies of almost eight hundred of which were found in a mass grave in an abandoned Victorian sewer under the institution in question in Tuam) that the idea of allowing the DUP into government in Ireland when they insist on creationism as public policy in Northern Ireland (there is literally a part in the visitors centre by the Giant's Causeway that says it's a basalt formation formed in volcanic activity 60 million years ago
or God Made It Like It Says In The Bible because of the DUP). The way that the DUP maintains links with terrorist groups who did
not agree to disarm as part of the Good Friday Agreement is also something that nobody here wants any part of. But it wouldn't be possible to just take NI without the DUP so, honestly, between the pricetag and the T&Cs, I think you'd have a hard uphill slog to argue for reunification here. In NI, not so much, there's been recent tipping over towards the idea because of the DUP's handling of Brexit, of Covid, and of some financial scandals that preceded both and which collapsed the NI government for months
right when it was needed to deal with Brexit and Covid. But both sides of the border have to agree before reunification, so the nightmare scenario is now on the table that NI could leave the UK, but Ireland wouldn't vote to reunify. And that's a nightmare because NI isn't a self-sustaining entity.