I kept thinking about this while I took my shower, and I think the "extroverted kids shouldn't be homeschooled" notion stems from a lack of awareness about all the options for group interactions that kids can get as homeschoolers. Being locked in the house alone with an extroverted child would be bad. But no one does that--not even the people with introverted kids do this!
Here's a list of things that my homeschooled kid has done that involved other kids. Note that in nearly all of these, he can talk, play, and interact with kids without being shushed or having to raise his hand to talk, thus actually giving him more time to exercise those "chatty muscles" than he might be likely to get in some classrooms:
art class
group piano lesson
swim class
sports teams
Boy Scouts
enrichment classes for gifted kids
foreign language lessons
homeschool group activities and park days
homeschool co-op
YMCA classes (including art, cooking, science, etc., not merely sports)
homeschool gym class
library events
chess club
First Lego League
zoo classes
summer camps
This is just what pops off the top of my head from our personal experience. There are lots of other groups that we haven't used (church groups, 4H, etc.).
It takes a bit more creativity, granted, but it's possible to get lots of social stimulation for a child if you have the time and the money. (Though none of these was expensive on its own for our budget. I'm a cheapskate!)
