Well, I can speak to this since I work for a company that does this. The improvement in microscope image analysis by computers in the past 5 years has been amazing. If the trajectory continues, I would say that 25% of image analysis will be automated using DNNs and other machine learning techniques.

Areas where it won't work: any time you have new image data that doesn't resemble what the networks were trained on. In fact, most people in the field recommend training on and running inference on a single microscope and if you change scopes, you have to retrain your model! Obviously data augmentation has a lot to contribute there but there a ton of challenges.

I've actually proposed building a warehouse-scale microscopy facility within a couple miles of amazon or google data center with full realtime reinforcement learning loop. If you have hundreds of near-identical scopes collecting the same data, you can train over the variation.