The Stourbridge is short and slow, so that a vehicle with 10 or so seats and a top speed of about 30mph provides a good service. I don't think there's any other rail route in the UK with similar characteristics.
Yes, the Stourbridge branch is a bit unusual, which is why it was chosen to test out the technology using a small-scale vehicle. But the test has been successful, and with that validation under their belts it appears from their website that Parry People Movers reckon that more capacious, faster vehicles using the same principle would also be viable, which increases the number of lines they would be suitable for.
The title of the thread suggests that there is something "wrong" with the Stourbridge vehicle using a flywheel rather than a battery for energy storage, when in fact it is a very suitable technology for the application. As long as it can store enough energy for a long enough time for the requirements of the service - which in this case it certainly can - there's really no reason
not to use a flywheel instead of a battery. It's all good solid old technology which has been in widespread use for a very long time and is thoroughly proven (what is being proven with the Stourbridge experiment is basically the putting together of those particular already-proven components in a particular way for a particular use), it is straightforward to maintain, and it does not use any exotic materials/chemicals/techniques of manufacture.
Flywheel storage also has the major advantage of a very fast recharge time. As everyone has pointed out, the major difficulty with battery storage is the conflict between the slow recharging and the need to keep the service going. With flywheel storage this does not arise as it can be recharged rapidly during station stops without interrupting the service. (Yes, I know the Stourbridge vehicle doesn't do this and uses an onboard engine instead, but the reason for this is to make the trial possible without calling for any commitment or expenditure on the part of the railways to install charging points, which would mean a battery vehicle would also have had to use an onboard engine.)
Using that advantage would make it possible to use flywheel units on all kinds of duties that involve long running times with lots of stops, like (first one that comes to mind) the Heart of Wales line, topping up the flywheel at every station. A battery unit on the other hand would struggle to get enough range to complete the journey in the first place, and would need at least twice as many units to provide the same service since they'd spend at least half their time recharging or being taken to be recharged. Flywheel storage can be used to effectively "electrify" lines in situations where battery storage is difficult. (Flywheel storage does of course need charging points installed at stations, but it doesn't need the huge kerfuffle of full-scale knitting which would be a bit daft on something like the Heart of Wales line.) The thread title implies that flywheel storage is some quaint oddity similar to clockwork and batteries are invariably and without qualification a superior choice, and my objection is that the modern tendency to automatically consider only electrical solutions to some problem and reject non-electrical ones without thinking because they're somehow not swish enough leads to good ideas being rejected and sub-optimal alternatives used instead, and rejection of flywheel storage is an example of this tendency in action.