I'm inclined to agree with your sentiment, but the example given doesn't quite sit right with me.

"Often a sentence fragment missing a verb (like this)."

vs

"Often a sentence fragment is missing a verb (like this)."

We still have short sentences which seem to make sense without a verb. Is the following grammatically incorrect? "Hello there!"

"Spoken English" being the key phrase there; if you use spoken English in a formal document or letter, it may reflect poorly on you.

Comment sections on the internets - and acknowledgements - are a bit milder on those grammar rules I'm sure.

"What nonsense"

That's an example of idiom. The word "what" is overloaded to mean "that is" - for dramatic emphasis.

The verb "to be" is often overloaded or implied in many languages. For example "quelle surprise" in French.

Perhaps we are dealing with a point of vocabulary. When I first learned Latin, we had "Civis Romanus" and "Mentor" as initial textbooks (kivvy was red and mental was blue). Later on a green book was added and it dealt with idiom (idia/idioms?) and I think that was its name, but I had moved on by then!