Except at that time migration was a relatively hard process and quite time consuming so those who migrated had interest in migrating there to conduct business. Not just to come to the streets paved with gold.

For the last 20 years across the whole western world we have seen that despite having more migrants than ever, the cities are not becoming cleaner or more vibrant - but rather everything goes backwards.

Ancient empires, early 20th century USA etc. succeeded not due to migration but due to government and people willing to work for the government to make it more successful.