Given how minor a road the A35 is- busy perhaps, but it is narrow, twisty and goes through villages, not round them- there's an implication that the transport corridor is either
A: low in demand
B: hugely underserved and in need of massive investment to unlock demand
or
C: goes through a very beautiful and topographically difficult area which a major road would have a big impact upon.
I suspect there would be _huge_ objections - and rightly so - if they were to build a major highway through coastal West Dorset.
There must be significant demand from Bournemouth to Devon and Cornwall - if you're driving you live with the A35, or head north from Dorchester to join the A303 (if that's any quicker - not sure), but rail is difficult. Practically, if a curve at Dorchester is impossible maybe they could build a Dorchester Junction station to the south of the town where services could reverse, then a curve at Yeovil.
However in the current climate there is (sadly) no appetite to improve railways purely for the leisure market - not enough profit in it - so the chances of it happening are approximately zero. You'd also get students I suspect travelling to and from university, but again, that would be restricted to certain times of the year.
Going back to that "building a railway network from scratch" thread, I suspect if we started over from scratch we'd build a South Coast Railway up the Stour valley towards Gillingham from Bournemouth and then follow a route similar to the existing Salisbury-Exeter route.
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