Because the route would be a useful interregional through route. Okehampton has already proved that there is demand in the area - this would likely be greater for a route via Tavistock to Plymouth.
For what it's worth I've always thought that Tiverton got a raw deal with its parkway. If there were decent local support for reinstatement (as there is for Tavistock) I would absolutely support it (same goes for the South Dorset/Devon branches).
It also allows trains from Waterloo to be extended to Plymouth.
Whilst not the best way of increasing capacity on the face of it, there's little other choice (OK you'd need Crossrail 2, Woking & Basingstoke junctions and redoubling of the WofE line - but that's more achievable than extra capacity into Paddington).
In a post Crossrail 2 world of should be possible to speed up the journey time (first off your save a bit by bit having to wait for the oncoming trains), a fair amount of that time saving would be a new limited stop service (Waterloo, Basingstoke, Andover, Salisbury, Yeovil, Honiton, Exeter Central, Exeter St David's and then through to Plymouth with limited stops) which whilst probably wouldn't match the B&H line on the on the train time but would be able to leave London later and arrive to Plymouth sooner (only just).
Whilst that's not likely to attract a lot of new passengers, there's likely to be a fair few added from SWML stations (it's not always very quick to get from them to Reading, so a direct service from Basingstoke would be fairly popular).
Places like Southampton and Portsmouth would be 1 change (Salisbury) from Plymouth and probably quicker than currently (even using the XC services to get to Reading)..
The potential of long distance services using the route want included in the cost estimates (most likely due to the fact that they required other investment - which is reasonable at this point, but could be a useful exercise to understand the bigger picture as to how the whole would be bigger than sum of the parts; however that would require joined to thinking and long term planning!).