From a marketing point of view this might have a niche. From an engineering point of view I have a couple of concerns. This would use space normally alloted to insulation. The slamming of the doors might cause chronic breaking of glasses.

Since water storage takes space within the fridge you might ty either storing water in an inside rack full of glasses of water or have a stack of plastic glasses inside the fridge which takes up little space.

Or, at absolutely minimum, store your glasses closer to the fridge. Ours are stored right next to it, pretty well.

JSH, I want to extend the door 3 to 4 inches outward thus leaving the insulation of the door intact- you are right on the breakting of glasses. That would need to be addressed but I think it can be over comed. Sand, my kids are always wanting milk instead of water. Cat, the kids can't reach the cabinets. All good input though!

Pre-pour the milk into small plastic cups. The kids won't break the cups. They won't waste the milk by spilling it as they pour it. The cups and milk will share the same storage space.