Well, the Kingsguard are a somewhat different case from the Night’s Watch. A small bodyguard doesn’t need to reproduce itself in the same way that a standing army does, so that’s not a drawback in the same way.
I think your suggestion kind of points out some of the benefits of the current system – if Kingsguard had families with them in King’s Landing, would they be looking out for the king or for their families? What happens if someone kidnaps their families and threatens to kill them unless they murder the king or leave the king vulnerable to murder?
Serving for life is a bit strange. If the point is to have the perfect bodyguard, why would you want someone who’s passed their peak fitness still on duty? Keeping them around to train the next generation and preserve institutional memory is a good idea, but when you’re limited to seven people, it seems a bit odd.