I'm not sure I agree, primarily because "better" is subjective.
A pipeline with template matching is extremely effective at extracting fixed form text in a standard layout, such as telephone numbers or credit cards, and computationally cheap as well.
But I presume a drop-in black box model which isn't bound to a low computational budget, can output plenty of false negatives and false positives, and can run on a single pipeline might be preferable at least from a product management point of view.
Also, neural networks looks good on resume while template matching doesn't. Just like statician/image analyst looks lukewarm but AI engineer looks superb.