DARPA funded the basic research. Then the actual Internet was largely built by for-profit private sector companies. That hybrid model seems to usually be the most effective for major new innovations.

DARPA funded most of the grant money used by research entities to create the various parts of the IP stack. That's not "basic research". Simply put, were it not for DARPA, we wouldn't have the Internet of today. We'd probably have something like it, but something a lot more closed off and walled garden-esque.