A lot of people are missing that there are variables here that make it hard to put just one parenting style on all children.
The OP mentions interfering with friends and that's the only thing that I actually have a real problem with. Unless a child is in danger, it's part of socialization for them to find and make their own friends, and to sometimes come home crying because they've had a falling out or what not. Do not tell your child who to be friends with and do not stop them from being friends with someone who isn't a danger to them. (When I say a danger to them, I mean, people who are a lot older before the child is 18, ones that are actually abusive, etc. and even then there are ways of dealing with this so that your child can come to the conclusion before you actively interfere).
Even that has it's down side. You can't tell all parents that because there are disorders and such out there that means a child can't manage their friends. My brother and I have ASD and we could never break things off with friends even when they were emotionally and physically abusive. We needed help. Younger brother however is sassy as anything when someone so much as annoys him and has no problem making new friends afterwards.
With the talk of University open days, I rolled my eyes a bit. Saying that it's a lack of independence to go to an open day with a parent is ignorant and, depending on the university, can actual exclude your child before they even get there. If they're nervous the won't be paying proper attention, if they need another opinion there's no one there for them, and they might not have a friend to go with as their friends might not be looking at the same university. If they go to that uni, it's possible they will get questions from other students on the first few days about why parents weren't there (I had this and had to explain I decided to come with a friend instead and got labelled as arrogant until about half way through the year) because most people come with parents. When I was working as a tour guide during my second year, only about 1 in ever 10 groups (6 people per group) had someone, who wasn't a mature student, without parents with them.
Like I said, I chose not to go with my parents. I decided I'd rather go with a friend and see the university and the town and have some fun. Not every potential student is going to want to do that. Researching the university (looking for culture) and asking your child is key.
Some things in this thread are unreasonable. People take parenting to the extreme both ways.
One thing I really want to point out is parents saying "no" to a request to make something such as drink or food.
I'm not saying make it for them either. Ask them why they can't do it. Do they not know how? If so, offer to show them. THAT'S YOUR JOB. If you don't have time to show them at that time, tell them to get something else for themselves instead and you'll show them later. Teach your kids how to do stuff for themselves, don't just expect them to know how to do it.