Would you support Ireland ending the common travel area with Britain?

I think you might be responding to something someone else said, or maybe something that popped into your head, but none of what you said in that post has any connection or relevance to what I said. The CTA is a mutual arrangement, within which Irish people have the right to travel freely to and within the UK, as well as the right to work and study. Allied to the CTA are other arrangements and rights, including for example the right of Irish citizens resident in the UK to vote in national and local elections. These are rights given to Irish people in law and vindicated by the legal institutions of the UK. In that regard, it isn't remotely clear what you mean when you refer to protecting the rights of Irish people.

Also, I repeat, if we go along with your suggestion that "the relationship with them should be ended", that'll also end the relationship with us - meaning we will leave a lot of Irish people who are currently resident in the UK with no rights to live and work there any more, as well as imposing passport checks and delays on people travelling between the two jurisdictions. You might be happy to be chucked out of Scotland, or else live there at the grace and pleasure of the authorities over there, but a lot of other Irish people living, working and studying there would not.

And also, if we get rid of the CTA we create documentation and identity checks at the frontier. And as I am sure you are aware, there is a 499 kilometre land frontier between the two passport zones on this island, on which there are at least 208 crossings. The Irish government and the European Union have spent the last 5 years trying to figure out how to prevent goods and identity checks at that frontier in the EU-UK Trade and Co-operation Agreement. The difficulties involved doing that are currently headline news. Removing the CTA would render all of those efforts pointless.

So, no, the suggestion in your OP is a really, really, really bad idea, and it is highly unlikely that any substantial number of Irish people would agree with it.

Why would someone travel to Ireland to enter the UK, when they could just get the ferry to Dover?

Forget Schengen. The CTA is needed so that Irish citizens have the same rights in the UK as British citizens and vice versa. Without that the GFA simply falls apart.

What is this "we don't need it" nonsense of which you speak?

and that other thing? Enhance? Borders? With our nearest neighbour?

Seriously? Have you not been following the news?

Personally I very much identify as Irish and European, but my sense of being European is not associated with the EU, more with European civilization. There was a time when I was an ardent EU federalist but my feelings toward the EU have cooled very significantly over the years, though I do not favor leaving it and I do not hope for its dissolution. I would align more so with the Polish-Hungarian view of things and dislike the way in which the western EU states are going, culturally and socially.

I also have a great affinity with Britain based on our shared history. I don't feel that Britain is a foreign country. In another universe I could quite easily see myself as happily Irish and British in a UK that worked a bit better for all the four nations and never broke up. If there was an option today for Irish people to claim UK citizenship as a birthright, I'd take it for cultural reasons. (I'm from a Gaelic, Catholic, southern family by the way).