The Internet that you're posting on was built on top of a military network intended to provide redundant communication in the event of a global thermonuclear war.

Responding to this part alone: that's not actually true.
The intent of arpanet, the direct predecessor to the Internet, was to make it easier for universities to use high powered computer resources located at national laboratories, as well as making it easier to distribute software updates. The person who initially pushed for it's creation wanted "an electronic commons open to all, 'the main and essential medium of informational interaction for governments, institutions, corporations, and individuals '". They secured funding for the initial computer science labratories, os research that underpin everything, and the foundation for the "INTERgalactic NETwork".

Arpa was, at the time, the advanced research project agency. They were under the DoD, but they filled a role closer to the NSF today.

In designing the system they referenced work done by people who were studying robust communication networks. At the time that meant the phone system and nuclear weapons. The research, however, was applicable to any unstable network, and so had particular interest to them because computers had terrible reliability and they wanted to not have to call people if they discovered they had turned off a computer halfway between New York and LA.

The closest thing it has to a cold war military objective is to help us win the research race and spite the Soviets. It can withstand a nuclear attack, but that's just because that's the easiest way to make it survive a farmer with a backhoe accidentally hitting a wire.