Questioning whether we are wanting, or ready to play in public is a worthwhile topic. Examples abound of various types like the shy individual who lacks confidence yet plays well and could possibly hide (somewhat) in a group/band. The opposite type is also easy to spot where it's all ego and not much music on offer. Between these two extremes there are lots of gradations coloured by the individual's ambitions, personality, training, equipment, age, physical appearance, and that elusive element nobody wants to talk about: talent.
Those who have performed and had a connection with their audience can experience something profound that can touch them deeply. It's natural to want to share this joy and encourage others to have that experience. It can also be "addictive" as a buzz that's like no other. I experienced this for the first time at age 14, even though I'd consider myself a shy type. Why is it that difficult? Well, obviously there is the fear of making a fool of ourselves along with a lack of confidence which under pressure can compound the likelihood of fluffing.
Is performing publicly for everybody? If they are forcing themselves to do so, are they as likely to experience a euphoric moment, or just be satisfied that they got through it... as an accomplishment with some degree of satisfaction?
(IMHO) there are two very separate issues of just being satisfied with an accomplishment as compared to having a connection with an audience. One is being on stage playing music, which others can hear, the other is reaching out beyond the stage and giving listeners a personal experience/communication.
All of the arts are about communication. Writing a manual isn't the same as writing a novel that enters your mind and brings thoughts, pictures and emotions. Music is no different as it can be presented precisely... like a manual, or it can be something that enters the listener's mind and evokes so much more. Great composers wrote music capable of this, but it still takes a great orchestra/band to deliver what's inherently possible.
If we are in the realm of improvisation, then it comes down to an individual's ability to GIVE those stories and emotions to an audience. Technical ability can allow us to deliver the goods, but too often technical ability is mistaken as the message rather then the means. This has been too long a discourse, so we'll just leave it there for anyone who has managed to get this far to ponder.