Brexit was a vote by Britain to lose all influence in its largest export market and instead hamper its industries with dual regulation and increased barriers to trade. Nobody thinking rationally would think it was a good idea. The referendum passed because people were largely ignorant of what Europe actually is and because the referendum put a boring, complicated state affairs against a fill-in-the-blanks fantasy option.
The fact that they had literally no idea what would happen to Northern Ireland after Brexit tells you all you need to know about how well considered the idea was.
Part of this is down to the politicians who were running the show - David Cameron, the prime minister at the time, thought the referendum was a good way to put the issue to bed - you've had your vote, we're staying in, shut up.
He more or less directly said that they weren't going to make any concrete plans, because he thought the idea was so bad that they weren't going to spend the money on them, and because releasing explicit plans would probably just give ammunition to the 'leave' side. It certainly would have torpedo'd one of the major arguments of the 'remain' vote, which was that a vote to leave was a vote for uncertainty.
So in that way it was a self-fulfilling threat - you don't know what's going to happen because we refuse to make a plan!
> The referendum passed because people were largely ignorant of what Europe actually is
This too is a failure of politicians over several decades - the EU was always 'them', not 'us'. It was something that happened somewhere else. It was convenient to blame the EU when UK politicians couldn't or didn't want to fix something. MEPs were always pretty anonymous, unknown by local people who then (predictably) didn't turn out to vote in EU elections very much.
The fact that they had literally no idea what would happen to Northern Ireland after Brexit tells you all you need to know about how well considered the idea was.