You'd be surprised how many times I've replaced a GBDT with logistic regression and had negligible drop off in model performance with a dramatic improvement in both training time as well as debugging and fixing production models.
I've had plenty of cases where a bit of reasonable feature transformation can get a logistic model to outperform a gbdt. Any non-linearity your picking up with a GBDT can often easily be captured with some very simple feature tweaking.
My experience has been that GBDTs are only particularly useful in Kaggle contests, where minuscule improvements in an arbitrary metric are valuable and training time and model debugging are completely unimportant.
There are absolutely cases where NNs can go places that logistic regression can't touch (CV and NLP), but I have yet to see a real world production pipeline where GBDT provides enough improvement over Logistic Regression, to throw out all of the performance and engineering benefits of linear models.