I've seen many examples where networks are trained on thousands or tens of thousands.

The most common example is digit recognition with the MNIST dataset. This is a common problem given to beginners, and even many beginners to CNN's achieve human-level accuracy. That dataset is in the tens of thousands.

there should be a push towards adapting CNNs to calculate/predict how the object might look under different conditions

Data augmentation like rotations, horizontal flipping and random cropping are a widespread practice.