Without Mumbai, Maharashtra is not different from UP and Bihar. And if you talk about Mumbai, then it has been flourishing right from its creation. It has the potential to become one of the top cities in the world. But this can happen only if more people come to Mumbai. More people means more tax to government. Do you know out of total tax collected by the Indian govt, 40% comes only from Mumbai.
Instead of discouraging north indians to enter Mumbai, politicians should invest more time and energy in continuous development of the city.
Calcutta had similar problem 30 to 50 years ago. Look at them now.
If you block Mumbai from north indians or any people, then I am sure after couple of decades, Mumbai will become Calcutta and some other cities like Bangalore, Hyderabad or may be Patna will become Mumbai - the hub of developmental activities.
Development of any city lies in the hands of its people. I am from Bihar, lived in UP for a couple of years, have spent 10 years of my professional life in Mumbai before coming to USA 5 years ago. I am called indian (with respect) here and used to be called bihari (with disrespect). But I have learnt in my life that- More people means more strength to develop its cities. Now it is upto the politicians of Maharashtra to decide. People will adjust accordingly. This world is a big place for all of us to live.