Mine tend to be a mix, but possibly leaning towards the more introverted side in regards to how large their friendship circles tend to be. This is due to me being a heavy, heavy introvert, and extrovertedness is just something I can't comprehend or empathize with very well. It is true that extroverted types seem more valued in the US? From personal experience most people see introverts as unfriendly, mean, or shy. Some also think it's an immature phase that you go through, "yeah, I was introverted when I was a kid too. Then I got over it."
Everyone always called a mean kid because I never talked to, or wanted to hang out with anyone outside of my one or two really close friends. Same with never wanting to attend parties, or be around large crowds. As an adult I learned to constantly have this dopey, blank smile on my face because everyone likes that sort of thing, and sees me as a friendly "simpleton" (their words, not mine) rather than a mean/snobby kid... which is easier to deal with. Less hostility, you know? Sometimes I wish I could be extroverted just because it's such a pain in the ass to get drained from being around people, and being considered weird, but eh.
It's difficult to get others to understand that introverted people aren't assholes, socializing in general is just very draining.
Anyways, sorry for the unnecessary tangent! This topic is a personal one for me.
My introverted characters are sort of like me, one of my MCs is also a huge introvert, but they're better at dealing with people thanks to experience. They can also last longer in a crowd, I tend to run off after 30 minutes if I can. Personally I'm cool with any type of character, either one I've been able to relate to as far as problems. (unless those problems involve not being popular enough, or being lonely when not around people) Can't say much about the "physical vs. mental" thing, I think they can go hand in hand if that makes sense. If you take better care of your body, your mind starts feeling a little better to, and vice versa.
I myself started feeling a bit more confident in dealing with people after I started working out regularly, but I started working out when I stopped being super insecure about my body. Imo an extroverted person can go through just as many mental hurdles as introverts, although they may handle those problems differently.