Wa'alaikumsalam.
There's no ayah or hadith that mention "husband and wife must live with the parent" or "husband and wife must not live separated from parent". It's mean there's no prohibition in Islam for married couple to live separated from their parents. But also there's no prohibition for married couple to live with their parents.
Joint family custom that you are talking about is based on cultural, not based from Islam because Islam does not govern where married couple must live.
Which is better for married couple, live in joint family or live in their own house, separated from parents?. The best is live separated from parents because married couple should build their own independent family where they can manage the family without intervention from other people. But of course, not every newly married couple have house or afford to rent a house. If they still haven't afford to have their own home, it's okay if they live with parents. But they must try to collect money to make them can have their own home through buy or rent.
By the way, culture in your place and in my place is different. In South Asia, after getting married, the wife join the husband family, while in Indonesia, after getting married, the husband join the wife family. That's why, in my place if married couple haven't afford to have their own home, usually they live in the wife parent's home. I myself already had a house when getting married, but for first few days I live in my late wife parent's house.