There are certain variables at play here.

1) My preferred method of communication is via the written word.

2) Just because an introvert is not shy and can communicate clearly (via the written word or in person), it doesn't, as you rightly point out, equate to a desire or liking for social interaction. I am fairly agnostic about such things, and will fall into sullen silence in social situations, should the topic of conversation prove superficial, banal, or an interminable deluge of small talk. Nor will I hide my boredom or contempt for the inanity of said exchanges.

3) Whilst I am capable of interaction in person and become quite animated if the subject is one of interest (cinema, literature, art, history, sex, psychology, metaphysics, religion, aliens, cults, conspiracies, dark jokes, satire etc), I find it utterly exhausting and draining, and require significant recharge afterwards by being alone. By contrast, the extrovert persona gets recharged by being around other people.

So no, I generally don't go out much (cinema doesn't count).