Was there ever a route that "00700 NOT VIA LONDON" was valid on that didn't go via Barnham (for which the "VIA BARNHAM" ticket is valid and cheaper)?
If the NFM64 list is accurate, there were only "not via London" tickets between Brighton and Woolston in 1996. Since then, a "via Barnham" route has been created, and the regulated fare has been switched to it. I don't know when or why either happened, but your answer may be in there somewhere.
The original poster
@LondonJohn asserts it's valid but there isn't any explanation as to why it's valid and the question is never actually asked;
afyutr asked a straight question and got a straight answer. Whether the answer was correct or not isn't something I can comment on.
That thread was written before the NFM64 data was published, so there was more variation in how people carried out fare checks.
I’ve found out that a SWR Duper Off Peak return with a railcard from Waterloo to Southampton is £26.40 and this is marginally cheaper than the ticket I have with the Clapham Waterloo add ons but it’s more restrictive in times so not an ideal replacement.
I should add that, if you have a Zone 1-3 season ticket, a Boundary Zone 3-Southampton ticket (or Wimbledon-Southampton, if Boundary Zone tickets are a pain to buy) is a bit cheaper. It has the same restriction code as the Waterloo ticket, but I don't know how exactly they work for a train which isn't timed to stop in Wimbledon.