Yes, that's the biggest thing that's under-stressed about exercise: the benefits are not just physical/health related. Like you, exercise has made me far less averse to interacting with people, and resulted in me being more outgoing, more open meeting new people, and just living a better life as a result.
There's a book called Spark: The Revolutionary New Science of Exercise and the Brain that relates that if exercise came in pill form, it would be plastered across the front page, hailed as the blockbuster drug of the century – purely on cognitive/psychological benefits alone. That really drove it home for me.
Don't just workout for health reasons. Workout for life reasons.