It's not really contrived, as sudden medical breakthroughs can happen. In Trek it could be even more common, as some flora on that newly explored world of Omicron IV just happens to have medical properties unfound elsewhere.
It depends what you mean by "sudden". If you mean a few years, then yes. But it could never happen in a few months. Even if they find some plant that cures everything, there's still going to be tests to isolate the active ingredient, trials to determine exactly what it does, seeking approval from the FDA and what have you. It's just not a fast process.