It should be remembered that railway route closures started before the Beeching act, and that while the loss of the services was often highly regrettable, British Railways was losing money hand over fist. Closing routes like the Churnet Valley line which were downright unprofitable seemed like a good way of tightening the purse strings (let's not go into the conflict of interest with that Marples bloke, generally thought to be the actual villian of the story).
Trains from Stoke to Alton might conceivably enhance the tourist appeal of the area, but aren't ever likely to be a viable means of getting to the park. The Churnet Valley Railway (and Moorland and City Railways if they still exist - I forget the exact situation) currently have track in place from not too far south of Leek at Leekbrook Junction to Oakamoor, as well as potential to reinstate the disused line from Leekbrook towards Stoke. Their priority at the moment is to build a station at the south end of Leek, which they're fundraising for now.
I'm not going to spend time backing this up with research at this time of night, but my understanding is that to run trains from Stoke to Alton would at a bare minimum require the following work at vast expense:
- Reopening the line from Stoke to Leekbrook to passenger carrying standards.
- Reconnecting said line to either Stoke station or a separate platform/station.
- Upgrading the track already in place south of Kingsley and Froghall (the CVR's southern terminus for passenger operations at present) to Oakamoor to allow operation of passenger trains over it.
- Reinstating track from Oakamoor to Alton - I seem to recall there being a tunnel involved at Oakamoor, the restoration of which could in itself consume a substantial chunk of cash.
It would likely also be necessary or at least prudent to:
- Reinstate the passing loop at Cheddleton station (the railway's HQ) and resignal much of the line to increase the number of trains that can operate simultaneously.
- Clear the carriages etc. currently stored at Oakamoor to an alternative location on the line, likely requiring new sidings or a shed.
- Devise some means of getting people up the hill from Alton station to the 'resort', particularly as the park entrance and hotels are on the opposite side to the end I believe daytrippers on the numerous excursion trains would once have come in through.
Assuming all of this can be done, your train departs Stoke and heads to Leekbrook, or more likely Leek, then reverses and takes the Churnet Valley line to Alton. That's a less than direct route compared to driving. Things get worse when you take into account that as it stands, a good deal of it (potentially the whole lot) could also be subject to a 25mph speed restriction too, thanks to the CVR operating under a light railway order like most heritage railways, and that obviously further increases your journey time. I'd guess at an hour or more in each direction.
Ultimately, while railway preservation has a habit of proving the word 'never' to be a bit strong, in this case I concur with Speedy that it'll never happen.