Why don't I have a custom title by now?!
No deny about that, everybody knows about the DARPA story and stuff. However initially the only institutions using the Internet on any large/visible scale were research centers and universities, as well as telcos, and international links were done on "bona fide" deals. The people operating them were also largerly bred from the early years of hackerdom, and don't forget how wild places like Usenet and BBSes got, with their alt.sex.* discussion groups and their philes ;-)
Not sure what that has to do with my statement and it's a half truth at best because the internet was initially a military experiment and is continually augmented with a lot of public funding on research
Especially during those first years (we're talking about a period spawning nearly two decades though, from the days of PDP-11 minicomputers and early hackerdom to the early days of the www, where the Internet truly went mainstream) government supervision, regulation and involvement of discographic majors was nearly non-existent.
Now, if control is indeed made stricter, then alternative protocols and ways uf using the TCP/IP infrastructure will be found. The problem with trying to "control the Internet" is that it's just like trying to prevent bits from being copyable: the Internet is designed to be just as unrestrictable as bits are designed to be copyable/transferable with the least possible ambiguity.
Sure, you can destroy DNS servers, you can order webpages to shut down, you can apply traditional censorship laws etc. but these are all half-measures that only scratch the surface.
The only way for gov and gov-approved media/service providers to regain some semblance of control without resorting to building another, parallel, entirely new kind of network (think of e.g. Minitel services in France), would be to start a sort of "gentrification" operation on existing infrastructure, by starting to provide content only over some new, encrypted form of gov- and corp- approved "darknet", only accessible with special cryptomodems.
Consumers would be give special modems with the decryption/encryption keys (even better: encryption could even be personalized per consumer, so packets would be always identifiable, but asymmetrically unlockable by the service providers), and would only communicate successfully with special receivers on the other side. Services and content would migrate on this new, parallel network over time, to the point where using "wild and free" internet would be of little interest to the average consumer, as it would be turned into a wasteland suitable only for hackers, subversives and deviants, while law-abiding citizens would only use whatever services are available on the "official" network.