My dad was writing code at the time, and he saw the big benefit as allowing developers to manage larger amounts of data on disk (10s of megabytes!) without a lot of the manual shenanigans and heavy wizardry in laying out the data on disk and finding it again. Plus, the industry thought the obvious future was languages like COBOL, what with their friendly English-like syntax and ability for non-programmers to get things done directly.
So little of that is true anymore. For a lot of things that use databases, you're expected to have enough RAM for your data. We don't distribute and shard because we can't fit enough spinning rust in a box; we do it because we're limited on RAM or CPU. A lot more people have CS degrees, the field is much better understood, and developers get a lot more practice because hardware is now approximately free. And nobody really thinks the world needs another English-like language so that managers can build their own queries.
TCP, on the other hand, is solving pretty similar problems: the pipes have gotten faster and fatter, but surprisingly little has changed in the essentials.
C is somewhere in between. A small fraction of developers working these days spend much time coding in plain C, and many of its notions are irrelevant to most development work.
But unlike SQL databases, you could ignore C if you wanted to; there were other mainstream choices. That wasn't true for SQL until recently; the only question was Oracle or something else. I'm very glad that has changed.