Yes, we can get rid of cavities. Advances in medicine and dentistry will mean that someday everyone will have a full mouth of teeth - cavity free teeth. Improvements in dental hygiene have led to many people being able to preserve their teeth for their entire lives. Someday cavities will be completely eliminated.
With good nutrition and proper brushing we can deter a lot of cavities. However, these aren't the only reasons people get cavities. Getting teeth to grow back is a great idea to get rid of the cavities that we do have, but obviously is only a fix and not a proactive answer. We will always deal with cavities, but may have a better way of dealing with them.
This medicine is a great discovery but it is far from being useful. There is no way to know how it makes teeth grow back and if they grow in in a way that makes the medicine useful to use. People cannot always get medicines they need, and there will still be plenty of tooth decay.
As long as there is candy, sugar, and poor teeth hygiene there will always be cavities. Some people are just too stinking lazy to take care their pie holes, and as a result of cavities, among other bad things, Will happen to these people. Good luck growing new teeth when you have ruined your old ones.