I'd have thought that along with the coasters the dark rides would be some of the most power intensive attractions on the park, given the number of effects and elements they have to keep running.
Solar power would be far from efficient for running attractions though. It's only recently that they have become truly stable enough to run home appliances, but even they have a mains supply to ensure the house still has power when the panels aren't generating enough. Aren't all those ones in EP's car parks only used to power the car park audio and lighting? Even then I'd question how much time is spent actually running off of the solar power, and not the grid. These rides aren't ran off a 240V mains plug you know! They use hundreds of volts to run (450V in Duel's busbar isn't it, and then there's all the effects and computers to keep going?). Most traveling models usually have a reduced consumption I believe which allows them to run off of generators, but even they can take up a whole lorry to be big enough!
The UPS and generators currently in the park will be there to allow for rides to end a cycle safely and quickly if the main feed goes down. Also, the PA' and emergency lighting will use UPS' as they are essential to safety and keeping guests informed (Though wether or not this is acted upon is another story all together!), but these will only be designed to last around an hour or so, not run the park under normal operation.
If power outages could be solved with backup supplies in every environment then we'd probably never hear of them anywhere, but it's not that easy. What happens if you're running a ride off of the backup supply and that fails on you? You've got no main supply to go off of, and you've used your backup option, so you're shafted.
It's not Towers' place to go around building generators and backup supplies for their attractions. It's the National Grid's job to ensure that the power supply remains as stable and constant as possible. Considering that many of these latest cuts have bought down the surround areas along with the park it would suggest that the problem lies higher up the chain than Alton Towers itself (Though it is undeniable that some bit of work need to be done internally over the coming years). Merlin can spend as much money as it likes upgrading all the cabling and infrastructure on site and have a state of the art utility network installed in the park, but if the power is failing between the power stations and the park then it is up to the Grid to resolve it and no amount of fancy infrastructure will fix that.
Hopefully both the park and the Grid will be looking into this and find a resolution soon though, as in these last few months the outages have been getting very frequent, compared to a few years back when it was quite a rare occurrence :/