It used to be that contractions were all but forbidden in formal writing. Then, in the mid-1980s, they began to appear in the news--and since, more broadly.
--Bruce Ross-Larson, Effective Writing
Hmmm. If it marked the end of ultra-formal writing, perhaps the Eighties was a better decade than I thought.
Conversational writing reaches readers. Formal writing is increasingly a thing of the past. And today, if you never use contractions, your writing will look downright weird, even off-putting, to a modern audience.