It is a long way (nearly 50 miles) from Westbury to Taunton on a main line with nowhere of significance other than Frome at its eastern end. There are already adequate (hourly) services from Weston to Taunton and this section is also a main line. Slow stopping trains on main lines through rural areas are problematic
It's a point of view, but we'd like to offer some counter arguments - there's more people there than you think, there are good reasons for rural rail services, and there is evidence to suggest that this particular route isn't problematic.
So first, there's more there than you think: we're talking I think about three stations (leaving aside the proposed Somerton station): Castle Cary, Bruton, and Frome. Frome is actually quite a substantial town, and (like many in the west) growing quite fast. In 2013, Frome's population was 27,203, and it's projected to grow by 25% to 34,000 by 2028. Bruton is quite a bit smaller, and truth be told if there is difficulty getting a compliant path we do sometimes pass. Castle Cary seems to be small at first glance (3,500) but bear in mind it is the parkway rail station for Shepton Mallet (10,000), Street and Glastonbury (20,000) and Wincanton (8,000). We have hinterland.
The reason why rural rail services get more respect now than they did in the 1960s is that we now better understand agglomeration effects - the way in which small settlements can behave like larger ones (higher productivity, more dynamism and innovation) if there is infrastructure that allows them to link up effectively. Rail is not the only way of doing that, but it is very effective (especially as you approach 1tph). Also, pollution from car traffic was thought for many years to be an urban issue - but studies on ozone and particulate pollution in particular have found real issues in rural areas too.
Finally, I would say a service is 'problematic' if it can't be done within normal train planning rules (ie there isn't capacity); if demand forecasting using standard methodologies suggest it can't survive without subsidy; or if performance analysis suggests that it would risk setting off 'cascades' of delays. We've checked all these issues, and we really aren't putting forward a problematic proposal (if we had been, I imagine one or both of NR or the ORR would have nipped it in the bud).