"In my experience engineering jobs are all about working with people."
I completely agree. In my relatively short (four years) but intense (four jobs, in four different countries) engineering/programming career I still haven't been in a situation where social interaction wasn't a daily requirement in order to do a good job.
At the very least you must be able to interact successfully with your fellow programmers, and your boss. Without being confident in your relationship with them, everything becomes more difficult, asking for help, helping someone, providing feedback, admitting mistakes and getting acknowledgment for a job well done.
In a large or very well organized company it might be the end of your social commitment, but in a good part of them you are likely to deal sporadically with customers, engineers from other companies, production, sales, technical support.
If you get to be known as "that guy", if you get to be known at all, promotions and raises become almost impossible to achieve, and in hard times you'll be the first in line waiting for the axe to fall.
Of course I'm talking in my experience, I have no doubt that there are companies where introverts can thrive. But is it to their (ours) benefit ?
I have been an introvert all my life, and getting a job helped me in being more open (in a "sink or swim" way) even more than making me a better engineer.