I feel like we need strategic dating sims, becase I'm growing tired of sweet talking girls into becoming my girlfriends...
So I would be supportive of this idea, if it gets to be well made

I will separate this post to two parts, one will be reacting to your post, second part will be my general idea of what should a girl/guy be in a sim dating game.
Hanging Out and Talking
When hanging out with one person, your friendship level goes up, but by hanging out with more people everybody in the group's friendship level goes up more then with one. And this is where we get into talking.
Um, I kind of like this idea, but it needs polishing. For example, do you think they will be grateful if you hang out with three people who detest each other?
In all seriousness, I like the idea of increased interaction.... But then I don't understand why would you kill it like this. Every person likes different things, has different hobbies... And even different friends and enemies. So if you pick three people who hate each other, their friendship with you shouldn't go up, but be prepared for an awkward day.
If you talk to Girl A and say you like sports, and then talk to Girl B saying you hate sports, then Girl A will realise you where lying the whole time and be reluctant to hang out with you again.
I wouldn't be prevented from hanging out with somebody who tries to be polite by "agreeing" with me on everything while "agreeing" with someone else on the exact opposite. I would just not trust him with serious matters. I mean, how can someone not being honest prevent me from having a good time?
Not to mention, later you are mentioning friendships based on common thingies... Do you know how boring it is to have a friend that is your second me?
It is completely natural for friends to agree and disagree on things and I see no point to why it should influence friendships in any hardcore way. The important thing is if they have good time together or not. And 100% common interests aren't important to have good time together.
The idea of having a family influence you definitely sounds good too. Bonuses or new people to know.... Definitely sounds interesting...
However, your concept fails in one exact point, in which every dating sim fails according to my opinion.
Friendship points are just numbers. Personalities are just variable influencers.
This is a completely wrong approach... And is exactly why dating sims are 1. easy, 2. completely unrealistic and 3. completely make no sense.
Because when the human factor is completely missing, that means there is some kind of an equation that breaks the game. And you only need to find it.
In most dating sims the game characters are pretty much separated. Your actions and interactions with some completely leaves another ones calm. I was able to nail one game which had 60 girls to become my girlfriends... You had like 7 locations to meet girls, each one filled with them every period of the day. But these girls were completely separate from one another! They were only mine and as long as I paid them a 20 minute visit once in 3 days, everything was alright. I could still date new girls, nobody would care... However, that's not how it goes in real life!
In real life you have to fight more.... If sweet talking is enough, the girl usually has a weak heart and you can pretty much play with her emotions however you like. But not everyone is like that, just as you mentioned in your post. They have their own interests, hobbies, things they like and things they find attractive... They also react differently with each thing... And there is always space for randomness, initiative from their side... They don't just passively wait till you meet them in the mall or park till it's their turn for you to meet them. The world turns around you in sim dating games, which is fine, but it shouldn't completely turn around you.
Which brings me to another chapter. I have to disagree with the task of finding one girlfriend/boyfriend and then as many friends as you can... Because everybody is different! If the girl is in love with you, she won't try to stay friends with you. Or maybe she will to not lose friendship, but her being in love won't be unnoticable. However, there's also personality trait involved, even here. Some are intricate and will attempt to disrupt your relationship to win you over. Some will try to steal your free time... Some will attempt to use their natural beauty to attract you and basically make you cheat on your partner... Some will lose friendship... You can't just plan to find one girlfriend and then make rest into friends just because you are already taken... Which is why such limitations make no sense either... Because even the hero has a personality, but unlike NPC, the hero's personality can change depending on decisions player makes.
Which is also another chapter. You can have a hero that is a complete playboy, will try to get as many gfs as he can or just screw around and have loose friendships. Depending on girls' characters, some may be alright with it, some may not. Or you can be a clear, pure guy waiting for his princess.
And of course, this is another point which many sim dating games omit as much as they can. Action and reaction. Or action and consequence. A complete fail in many dating sims, because the actions have an immediate reaction, which everybody can see.... But nothing subtle. However, in real life it doesn't work that way.
There are rumors that may influence peoples' views about you. People who may randomly see you with someone, which can bring up a suspicion towards relationship. Girls are often friends with each other in such a way that they at least gossip in huge circles. And of course, when you're alone with a girl, but have a girlfriend, when the friend of your girlfriend sees you two together alone, it is very suspicious... And I could continue.
I'm not going to continue though, because I would write too long of a post.
To wrap it up, this is what many dating sims are missing. A slice of life.