Unfortunately for your point of view the Republic is very much part of the EU and an open border with NI vital to it staying in the single market and its economic wellbeing (and vice versa). There's also the prospect that a return to a hard border will threaten the peace process and reignite the "Troubles".
On a technical note, Northern Ireland is not part of Britain but is part of the United Kingdom.
In 2016 we sent 43% of our exports to Europe - that's a very big chunk we're going to have to replace as "Global Britain". Distance is very important in trade, and will remain so. See the link below.
https://www.thetimes.co.uk/article/...-our-own-and-thats-not-a-good-thing-w6w6m5hdb
You're right. It is daft to leave the biggest and richest trading bloc in the world which is on our doorstep.
Also, knowing that we are in a desperate situation please explain why the rest of the world should do us any favours in any future trade deals, which in any case take years and years to negotiate ?