Looking that the Weymouth-Waterloo timetable I couldn't help but notice that whilst the off-peak Mon-Fri slow Poole-Waterloo takes 2hr44 mins, the opposite journey takes 3hr16 involving interminable waits at So'ton Central and Brockenhurst. Ok, so obviously you'd have to have good reason for taking either service when there are faster available options, but it did get me wondering. If the service from Waterloo continued instead of hanging around at either station it would still arrive at Bournemouth 1 minute before the faster one behind it. Also, why the dramatic pause at Brockenhurst? Sure, it waits for the XC to pass, but then stays there for another 19 minutes. I guess it's to even out the service pattern at stations between Brockenhurst and Bournemouth. Essentially it's three separate services - WAT-SOU, SOU-BCU and BCU-POO. I wonder how it's crewed.
There's definitely a crew change at Southampton in the down direction. Maybe up as well.
I think you have to look at the down direction 'all shacks' calling pattern west of Southampton in combination with what the relevant two 'fast' trains do.
The idea seems to be that if you want a station between Southampton and Brockenhurst, then you change out of the fast service that arrives at Southampton at xx21. You can also change out of the semi fast into the fast if you got on somewhere such as Eastleigh.
But as you rightly say, if you want a station between Brockenhurst and Bournemouth, then the two fast services are different. One of them runs non stop Brockenhurst to Bournemouth, and the other has a few stops at the relatively larger stations. So it is best to run the stopper following the faster of the two fast services, to balance the calls out around the hour at those stations that do get 2 tph.
I think that is the main reason why they don't run through on the opposite half hour. (In any case west of Brockenhurst they run in the path of the previous Brockenhurst to Wareham shuttle, so there's probably an element of leaving things alone.) It would of course be helpful if they didn't advertise the down service as being for Poole at Waterloo, Brockenhurst would be better IMHO - and I've put this in a few similar threads before...
