Minor side: the first thing I typed into the filter box was "save" because I wanted to see how the designer thought about the whole "floppy disk == save" problem in a greenfield icon set. I thought it was even more remarkable (or just notable, I guess) that there's no Save icon at all, which really speaks to where the world is at around cloud-based web apps.
Why require someone to click Save at all, right?
Sometimes saving is a high latency operation.
Sometimes you don't want to show others data as it is being edited, think product data for an online story. Heck the "reply" button beneath the text box I'm typing into right now is a form of "save".
Paradigms matter! Saving was necessary for all disk IO for a long time due to technology limitations, but even now days it is still the appropriate paradigm for certain circumstances.
In modern CMS workflows (used by e.g. newspapers), the software will auto-save draft versions; while you then explicitly publish particular versions (or, more likely, submit particular versions for the next stage of the pipeline, e.g. editing) by changing your latest version's state in a drop-down.
This process really has no analogy with saving per se. It's more like tagging a commit.
I'm someone who does everything that I possibly can while offline, and I'm mostly in the camp that the "Save" button being a floppy is not much different today than learning how to pinch-to-zoom or click a mouse (i.e. there's an up front cost to learning it, but it's already ubiquitous, so why change)
I've still got quite a few icons to release in batches. One is a floppy disk, but it won't be labelled as "Save" :D
There's a few options to take, but these days it mostly comes down to the context of what you're saving, rather than the action itself.
"Save Document", "Save Template", etc
I still Ctrl+S automatically though:(
It's like the 'close door' button on an elevator. Some people just want to feel like they are doing something.
As I understand, basically no elevators have placebo close door buttons, but some have ones that only function when the elevator has been placed in manual operation mode, which requires a special key and is usually only done for service, emergency operations, and other special circumstances, and in which mode doors do not close automatically.
Because you're making many changes to a large form and a partial update could result in someone else using bad data.
Of course, ten year olds today wouldn't probably understand its origins. But what in today's world could represent a platform-agnostic, general purpose, "Save" icon? A flash drive? SD Card?
Think about commit in git. It is the logical evolution of the concept.