Distillation is usually used today to tame its resource problems at scale - you run BERT to squeeze out maximum signal from your training data and then distill the model e.g. into cheap CNN for inference.
Inverted indices are very efficient. How much of that can you give up at what trade off? If I’m only going to be better for 10% of queries, is that a cost effective solution? What if I spend the same amount of time tuning a traditional engine a bit more and get better accuracy for 5% of queries? Tradoffs rule the world of practical search implementations.