The whole thing with passports is a bit of a red herring, for sure a passport isn't needed to travel from UK to Ireland for those nationals, in fact a passport isn't needed for all travel within the EU and a whole host of other countries, all you need is a nationally issued ID card. The passport complication arises because UK citizens don't have ID cards. As many have pointed out you just need valid photo ID, in the case of travel between UK and Ireland, and it's just coincidental that a passport is also a valid form of photo ID, it's just for most Brits it's the only photo ID they may have.
When travelling around EU (schengen or not) I never take my passport, my French ID card is sufficient.