I think it can be done for less cost and more time building the thing like you suggest. Where it falls down (Excuse the pun ) is when you want to alter the timing or have them operate in sequence or such. I'd rather spend £30 or so on a servo and controller than £10 on gears and motors and not know how to fix it all together. I think I am looking at the bigger picture of getting several targets to work together in a controlled sequence. But then I am biased as I work on industrial control systems for a living!
Lets face it there is nothing wrong with the string on the standard Nockover, but fully automated targets is a fun project.
Thanks
Mark