Instead the sheet is both layout tool and data "meaning" in one glob of garbage.
Apple tried to solve the issue with "Numbers" but ymmv on how well.
"Data laid out on a grid" is a paradigm that applies to a wide range of problems and spreadsheets are pretty much the only tool around that can deal with that entire paradigm. The user isn't stupid. The user has a use case that isn't being catered to.
This is probably a glass half full/empty at the end of the day.
Fact is spreadsheets don't scale because they are sloppy and they don't provide a clean coherent path to getting the user to scale themselves into a sql like solution.
Oh well.
Excel's tables are probably similar what you mean, but Microsoft rightly allow them as elements on each sheet rather than basing the sheet around one table.
Your "tiny subset" is your confusion at not seeing numbers I suspect.
Wikipedia actually does a decent job of trying to describe the philosophy.
Excel has Tables, which sort serve a similar purpose, but the sheet itself is a flexible grid with no pre-conceived purpose, which makes it much more flexible than Numbers.
For example, it's relatively easy to knock up a simple Gantt chart by directly coloring cells, something that I've seen often. And you could argue that it's not the best tool for the job, and you'd be right, but it's easy and does the job well enough in many cases.
And that's why it's popular and iWork isn't. Numbers concentrated on making charts and tables beautiful; Excel is a general-purpose programmable platform.
I would argue that the major benefits that a database offers over Excel is data integrity and consistency. I think the lack of that sort of constraint is a major aspect of what drives 'biz' people to spreadsheets.