Isn't OS X graphics supposed to be based on Display Postscript/PDF technology throughout? Why does it have to render at 2x and downsample, instead of simply rendering vector-based primitives at native resolution?
No, CoreGraphics just happened to have drawing primitives similar to PDF.
Nobody wants to deal with vectors for everything. They're not performant enough (harder to GPU accelerate) and you couldn't do the skeumorphic UIs of the time with them. They have gotten more popular since, thanks to flat UIs and other platforms with free scaling.
No, I think integer coordinates are pervasive in Carbon and maybe even Cocoa. To do fractional scaling "properly" you need to use floating point coordinates everywhere.
OS X could do it, they actually used to support enabling fractional rendering like this through a developer tool (Quartz Debug)
There were multiple problems making it actually look good though - ranging from making things line up properly at fractional sizes (e.g. a "1 point line" becomes blurry at 1.25 scale), and that most applications use bitmap images and not vector graphics for their icons (and this includes the graphic primitives Apple used for the "lickable" button throughout the OS.
edit: I actually have an iMac G4 here so I took some screenshots since I couldn't find any online. Here is MacOS X 10.4 natively rendering windows at fractional sizes: https://kalleboo.com/linked/os_x_fractional_scaling/
IIRC later versions of OS X than this actually had vector graphics for buttons/window controls