This is your idea of weekend fun, more typing? 😆
The things is that I never had the fortune of getting grandparent's love. Grandparents from my mother sides died before i was even born, and those from my Dad's side also left us when I was 1 year old or so. So, I have no personal experience with them, my post is just my opinion by the experience of people and how I have seen them with grandparents.
The problem of not living together has arose from the mass migration. People of villages want to go to city, people of cities want to go to metro, people of metro want to go to foreign, etc. They then have their family in the new places. But the grandparents have an attachment to their native place. I have seen some cases where they don't want to give up their own home to go live with their kids. Another problem is the rocket high cost of living in India, especially in urban areas. It's difficult for people to own a big place to live.
Living together also doesn't come without a mess of its own. The older generation feel as if they are losing the control, and any insult from their grown up kids might hurt them. Some kids do behave very badly with the old people, I have personally visioned one such case. Not to say that the children are always at fault, sometimes the old ones too take insult at any disagreement and make a big deal out of nothing.
Yes, kids are missing out on things. Grandparents have vast experience and they can guide you through many problems. They also are from another time, and it's fascinating to hear those old stories. It's a way of living those times we weren't here. I love to listen those recollections from my parents.
As to the control, that's where most problems arise from. As a kid we are used to our parent's authority, we also resent t many times. And there is hope that once I get independent, I will be truly independent. But even after growing up and having financial independence, if their parents still try to control them, it creates anger. I am never in favor of parents dominating, and this holds especially after the kids have kids of their own. They should treat them like adults living with them. They should discuss matter, give advice, etc. But let the grown up child make the decision. Forcing it at that age will only break the bonding.
I think the want to stay away has mostly to do with the shackles some might feel if their parents dominate them. They can't wait to be truly free. I sometimes can't wait to move out so that my mother doesn't nag me any more. Although career has it's place, it's not like they can't keep their parents with them later on.