I'm 23 and have lived most of my life without having close friends. I'd say I'm very extroverted and can strike up engaging conversations with most people I meet. I'm easy going and don't really have a fear of talking to new people.

The problem is that I end up with dozens of friends that I regularly have good banter with, but it just never feels like one of those "best friend" or "close friend" situationships. Most of my own problems or vulnerabilities are dealt with by myself, internally, perhaps with some advice from others if I discuss it. It feels like you need to lean on people emotionally in order to actually become closer.

What OP has mentioned does actually work and I have used some similar approaches, without knowing it, to improve my friendships. But you also need to attach a high value to regular conversation and communications. If you don't keep in contact on a regular basis, the friendship will diminish, regardless of the closeness.