The sentence is grammatically correct but unnatural. "the necessity of..." is formal "the need for sth / to do sth" is less formal. "use a pronunciation" sounds strange. "pronounce words" sounds more natural "a right..." is uncommon. If there is only one right way, then "the right way". Otherwise, people often say "a good way". This would be natural for a native speaker: "This is a good example of the need to pronounce words correctly."

the necessity of using 'the correct' pronunciation. Is correct English, you can say right but it is not correct. By saying right you are introducing some ambiguity. Although right means true a fact, it also has other connotations. does a pronunciation have any right?. does it have any rights? NO does a pronunciation have a correct and incorrect way of pronouncing the sound? YES do you pronounce words correctly? Yes Do you pronounce words rightly or truthfully? NO