The reason for this offpeak availability difference is that Peterborough is outside the 'Network area', unlike say Cambridge which is firmly inside. AIUI▸ for fares that cross London to a destination 'outside' the former NSE▸ Area morning restrictions
There are historical reasons at play as well. Cambridge is in the former Network SouthEast area while Peterborough is outside it. Fares policy and the types of fares available hark back to the pre-privatisation era with Cambridge being NSE sector's responsibility and Peterborough (although served by NSE trains) being InterCity's.
The Network Area is more than just historical, of course. In code 1T (and a lot of others, used across the country) there is this text under "General Conditions (for this ticket type)":
Off-Peak tickets for journeys
starting within the Network
Area to destinations outside
the Network Area with travel
via London are valid by any
train to London, to connect
with trains from London.
That applies to THA-PBO, and the time restrictions at KGX which it inherits are more generous than at other termini. If you apply that rule you'll probably find that from somewhere like Yeovil or Exeter the off-peak return to PBO is cheaper than the anytime to
PAD» and unrestricted on that leg. But in that case you get a different restriction code, to stop you doing that.
This follows:
Off-Peak tickets for journeys
starting outside the Network
Area for travel via London use
restrictions from the origin
station to London and return.
Unless shown otherwise, they
are unrestricted between
London and the destination
station, and return.
For super off-peak the wording is different, though the meaning is the same.
There is no text for off-peak journeys within the Network Area, even for THA-CBG, which is one. There might be a justification for a simpler rule with the same peak across the area, on the grounds that this is all commuter territory. But for the Network Area - Exeter to Kings Lynn - but not for other "metro areas", I don't buy that.
By the way, the super off-peak to PBO I now find is code 9D, not C4 as I said. However, that is even more puzzling in that it is less restrictive that C4 - outward peaks at KGX 3:00 to 9:05 and 15:00 to 18:59. However, it has a return morning peak restriction into KGX at 4:30 to 11:17, while C4 has none.
I can understand that the basic off-peak restriction is pretty regular for one London terminus, corresponding to when the system is fully loaded. I can also understand a desire to not apply all those restrictions to across-city journeys, which don't involve all that many travellers. But as applied now, it's still a mess. If all the odd differences are just a historical accident, I'd say that might be accurate as history but it's not a good reason.