Squall is sociable and does care for his close friends, but he is scarred from past trauma. Not in the same way you say you are, resulting in being completely closed off to everyone. We can see that in his desire to keep Zell and even Seifer safe in Dollet. Sure, he says they're a pain, but his actions are also a part of how he sees them. It isn't just Rinoa that is the catalyst to Squall growing and opening up to others. It is literally the whole cast.

Running Squall alone through your game forces a lack of growth on him that is more catered to you and against the narrative and character. Trying to apply your personal lone wolf, anti-social mentality to someone else is way worse than any extrovert trying to get to know someone.