Actually, it’s not! When we’re able to figure out what people ate before death, it’s usually due to preserved tissue in the stomach. Unless it was a pretty big chunk of food, the stuff stuck in teeth is usually not too helpful…unless it’s part of the decedent’s oral microbiome, apparently.
The oral microbiome is the “micro-environement" that’s formed by our oral anatomy, saliva, immune system, and, most relevant to that story, hundreds of species of oral bacteria. It’s something all of us have, and even though it differs from person to person, depending upon their immune system and diet, it’s not something you can (or want to) get rid of.
Buuuut…when you let it get out of hand, it’s also what causes lots of cavities and caries and bad breath. Plaque is largely dead bacteria, and tartar/calculus forms when that bacteria isn’t removed.
However! It’s good for us that ancient tooth care wasn’t amazing - analyzing old microbiomes can tell us about the diet and health of the individual, and can show us how oral microbiomes have evolved or changed over the centuries.