I mean, I hear what you're saying - but all of those things also seem to be a single discipline.
Otherwise, where do operating systems fall? Are they systems engineering? They don't seem to be entirely about the hardware to me, and they were a core part of my CS program. What about SeL4 - which is a formally verified operating system project?
How about programming languages like C or Rust? Is that computer science, or systems engineering? How about Excel - the world's most popular programming language - that happens to be functional? Are financial planners doing computer science when they program a spreadsheet?
The lines are blurry everywhere. My CS program offered 3 different degrees, like you said - Computer engineering, Computer Science and Software Engineering. The only difference was the CS degree had a lot of electives, and the other two filled those electives in with (different) required subjects.
Maybe CS is just "lets play with some cool things on computers!". And there's a big playpen of things to explore. Thats more or less how it feels to me.