Sure they do if they have their IT priorities right. There's a small business in my locale that I can't name that occupies one floor of an office, does all kinds of app development for big companies, and still allocates enough time to innovation that they regularly present clever stuff at conferences dedicated to what they do. That stuff also directly improves their competitiveness in most cases. People might say something similar about Jane St's Ocaml contributions that they turned into a side-effect of doing their business. There's been countless admins in companies with less vision that innovated plenty on semi-automating monitoring, management, and reliability just out of necessity to reduce stress on their overworked brains and hands.

There's tons of potential in companies for IT innovation, whether small- or large-scale. It's proven by those, even tiny firms, that act on it. Most companies act against it on top of under-funding, under-staffing, and over-stretching their IT staff. That combination causes the effect you describe. It's not inherent in any way. If it was, examples I described wouldn't exist.