It's not that unrealistic.
Think about it. People tend to make friends in school or at work.
He's rich and doesn't work. He likely didn't go to college because he had no use for it, so he didn't make any friendships there. He doesn't work, so he hasn't made any friendships there either. Even if he had made friends in high school, they're all likely married with families by now, so they're not stopping by to hang out, if they've kept in touch at all.
He's self-centered. He fills up his day by getting haircuts, or playing pool, surfing the internet, buying things, which are all activities that to others are not activities at all, but to him are things he can do to fill up a day on his own. He's able to keep himself happily entertained on his own. He's really not put into any social setting where he'd make friends, and he feels fine on his own and doesn't need them. He probably has friends he's met along the way, but they have their own lives so they're not constantly in his life, and his character enjoys being alone so he's not likely to call them up to hang out.
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