I don't think that it is clear that you cannot break these tickets overnight, for the following reasons:
1 - when I look them up on NRE they are described as "off peak". As we all know, following the great fares simplification of 2008, everything is super-simple now so I dutifully look up the T@Cs for "off peak" tickets on the ATOC site. There, it starts off telling me that "off peak day" tickets are only valid on the day on the ticket. It doesn't say anything about "off peak singles" or "off peak returns". As far as I can tell from publicly available information, my ticket is an off peak single. Anyway, it goes on to tell me that for "off peak" tickets you are allowed to break the journey unless conditions state otherwise. As far as I know as a member of the public no such conditions apply. And if I have the fares manual then I know that it is stated that break of journey is allowed. Going back to the "off peak" T@Cs, I am told that I am allowed to break my journey overnight as long as I continue before 12 the next day. So as far as I know from information on NRE, I am allowed to break my journey.
http://www.nationalrail.co.uk/times_fares/offpeak_conditions.html
2- On NRE it states that I can check the validity of my ticket on certain trains by entering the details into the journey planner and seeing if my fare shows up against those trains. When I try various journeys to Dublin that mean travelling overnight, my fare shows up against these journeys, which immediately flags the "valid on ticket date only" condition as contradictory. It seems that the best interpretation here is that this actually means it is valid for journeys started on the ticket date.
3 - as others have said there are plenty of journeys on the railsail tickets which are impossible without an overnight stop.
Anyway, I have just bought a £30.50 ticket from Ealing Broadway to Dublin. The national routing guide tells me this is valid via reading and oxford (well, a normal any permitted ticket to Holyhead is valid on that route, at least). I am now en route to Oxford where I am going to spend the night and I shall resume my journey in the morning, and see whether I get challenged!