I don't think extreme accuracy matters that much when dealing with large sample sizes. If the margin of error is under 3% (like opinion polls) then it's good enough for many purposes.
My comment above is not about statistical variation, it is about measurement error. Inaccuracies in models for labeling images are a form of measurement error. Having humans label a (often stratified) sample of images is required to understand the measurement error. This requirement is the main difficulty when it comes to generalizing learning from one context to another. If you use multiple independent humans to label all your images, you can understand the errors made by the humans very well.