Speaking as the Alpha SG (representing the setting), there are many potential problems with that proposition.
- It assumes that the child wants to become an apprentice to any of the members (or even at all).
- It diminished the incentive for a magus to go looking for an apprentice.
- It is incompatible with the traditions of some of the Houses (Tytalus with their hard training regimen, Mercere with the blood of their founder, Jerbiton with the Gentle Gift, to name just a few).
- It gives the apprentice power over their master ("if you don't do this I will lodge a complaint against you!")
- It may create ill-will between the magi of the covenant, if one of the magi convinces a child to become his apprentice instead of the magus who found the child
- Some might even say it is a deprivation of magical power, since you are infringing on the right to take an apprentice.
The best avenue for changing the way apprentices are treated would probably be the Lotharingian Tribunal, as this new Tribunal could set its own rules regarding apprentices.
EDIT: One more problem. "Loss of apprentice" is a punishment option for some crimes. Do we now need to ask the apprentice before we impose it? And to whom the apprentice is granted (usually the injured party)?