ARPA (before the "D" was added) funded a lot of the preliminary work you discuss (e.g. Engelbart's work at SRI was all government funded). They also essentially paid for the graduate school of all the folks who later did the early ARPANET work (which Bob Kahn at ARPA also paid for).

And consider that "private sector" labs like SRI and MIT are essentially government research facilities. Education is only 16% of MIT's expenditures (and 14% of revenues) and where do you think those revenues come from? Hint: most of it is not corporate grants.

Through the 70s the boundaries between corporate and government R&D were often fuzzy. True, Bell Labs wasn't "miliary-driven" but there were close formal and informal ties and remember that they were under a tight consent decree up into the 1980s. It wasn't today's "revolving door" -- think of it as a permeable membrane. This was thought to enable corruption and in the wake of the Viet Nam war some separation was put into place. Of course the resulting separation hasn't cleaned things up as expected; in many ways it's worse by shifting out of the technical and into the political domains.