If it’s reciprocal, yes. If they are not fit to live/work/study in another EU country, why should they be allowed? No different from the rest of the world.Are you happy that your kids/grandkids will at present have to apply for a visa to work/live/study in each and every EU country?
I wasn't interested in living/working in Europe. I went to South Africa. I was needed and qualified and wanted. No problem. What makes you think they will be worrying about not being able to work/live/study in the EU? Probably won’t even be an EU by the time my grandkids grow up.And can you tell us how you will explain to them why you didn't have to worry about that?