Here's an overview I did a while back which gives a flavour of what is likely to be required for my proposal:
Putting my hard hat on (in more ways than one)...
I have considered how you get through the centre of Radstock without the need for a level crossing. What I bear in mind is that, at both the Shoscombe end, and at the Midsomer Norton end, the trackbed is elevated, so you would construct an elevated section through the centre of Radstock to link them up, thus avoiding the need for a level crossing. Starting from the Shoscombe end, you would unfortunately need to demolish some properties along the line of route in the Waterloo Road area. Whilst this would be regrettable and undoubtedly controversial, I'm not sure I'd use the term "extensive demolition" - certainly no more so than (say) the demolitions at Galashiels and Gorebridge on the Borders Railway were. Then on the elevated section above the site of the former S&D▸ station you would build a single platform station accessed from the ground by fully-accessible lifts from a reconfigured public square that incorporates the current mining memorial, and would provide access to Radstock town centre, the new developments on the old GWR▸ station site, and the Radstock Museum.
I completely agree with rogerw that there are some bridges, viaducts and other structures right along the route I've identified that will need to either be replaced or strengthened. There are other issues too - For example, I personally don't feel that getting through Wellow on the original alignment is likely to be feasible, so a diversion arcing south round the village is likely to be required, joining up with the old station site (which along with Masbury further on if we go to Shepton would have to be purchased) where I feel a passing loop could be ideally situated, thus allowing justification for reopening Wellow station to serve a local population that has very little in the way of other public transport provision.
Midsomer Norton heritage activities I feel could fit with a reopened S&D, providing and stabling the motive power and rolling stock to run the kind of heritage trains that are part of the overall Borders Railway offer. Let's face it, the one thing you cant say is there wouldn't be a market for it. It would also provide another potential passing loop.
If we go to Shepton, then the cutting at Chilcompton would have to be cleared, and there are obstructions elsewhere here and there, such as the infamous Binegar Bungalow. At Shepton itself, there would clearly need to be intense discussions in terms of where the station would be situated.
However, as rogerw says, there is an engineering solution to anything, and as far as I can see, pretty much all of the issues above can draw on potential solutions deployed by Network Rail when constructing the Borders Railway.
So to summarise, I'd have a line that service-wise would be an extension of MetroWest, which from Bath would call at Bathampton (if built by opening time), Wellow, Radstock, Midsomer Norton and potentially Shepton Mallet. As rogerw suggests, it will require substancial funding, at least as much as the Borders Railway and probably a fair bit more, and would indeed require the same level of political that the Scots somehow found, but has been sadly lacking in this part of the world over the same period.
It doesn't mean its impossible though, and I live in hope.
A feasibility study would look at all of this in greater detail, tease out the aspects that may not be apparent when first looked at, and tell us once and for all whether it is a potential runner or not.