I do find the negative rhetoric regarding any railway reopening in this country disheartening, and typical examples can be seen in this thread!
However there are some good points, which I would like to both echo and add to:
1) If this railway reopens it will be popular. There is an insatiable demand for rail travel in this country currently, and frankly if you laid a new line from one side of a field to another folk would use it.
Yes, there might not be much local traffic from Bakewell to Matlock, but there is a strong passenger flow from Manchester to Derby, and also to Leicester, Loughborough, St Pancras and to a lesser extent Luton and East Midlands Parkway. Most of this is currently via Sheffield, except for a small proportion of Derby travellers going via Stoke.
However passenger numbers are stymied by the awkwardness of the journey; some people choose to drive via the narrow, twisting cart track that claims to be the A6; many more either choose not to go, or at least don't go as often as they would if a direct service was offered.
2) Okay Pyewipe, so why not run via the curve at Dore?
Well (a) it's long-winded. Look at a map, you wouldn't plot a route from Manchester to Derby via Dore. (b) The Hope Valley can't cope with the extra traffic, and even some further resignalling is unlikely to free up enough extra capacity. (c) Such a routing would create conflicting moves at Dore with negative impacts on Sheffield to Manchester and Sheffield to Chesterfield services, and (d) operators are unlikely to resist the traffic draw of Sheffield a few minutes away, and would inevitably start sending trains there to reverse again.
3) So why not improve the bus service instead?
Because most people hate buses. It doesn't matter if they're electric, diesel, hydrogen, hybrid or powered by the wings of a thousand angels. Nor does it matter if they have leather seats, USB ports, WiFi, a champagne bar or a jacuzzi. The travelling public will refuse to go on them.
Plus the faff of a train to Buxton, bus to Matlock, train to Derby. I'd enjoy it because I like buses; the ordinary traveller, not so much.
4) What about the cycle/walking route?
I'm old enough to recall that many of these routes were originally created to preserve the alignments with the hope of reopening the railway lines eventually. Indeed Sustrans used to release statements at the opening of each new cycle route to the effect that one day the trains might return.
Yet if you propose such a thing there's immediately a storm of protest!
Nobody will stop visiting the Peak District if the Monsal Trail closes. They will find other things to do, other places to walk or cycle. They might even use the reopened train service to access other attractions.