A study that concludes the problem cannot be solved as posed has usually saved a multiple of its own cost, and it almost always comes with an alternative: change the lighting, add a different sensor, move the inspection point, instrument the process differently, or accept that this particular defect is a process problem rather than a detection problem.
The alternative is a programme that runs for two quarters before the same conclusion arrives, by which point hardware has been bought and expectations have been set inside the customer's organisation.
This is also why a supplier who has never returned a negative feasibility result is worth asking about. Either the work is unusually easy, or the study is a formality.