“I know what to do; reduce block of memory assignment where the printer needs only horizontal slices, to, er, horizontal slices.”
Your naive analysis applied to the RISC OS port's examples results in the conclusion that Gutenprint uses less than one bit per output dot. Does that really sound right to you? Doesn't it seem more likely that they already use a divide and conquer solution and your "suggestion" is redundant ?
Of course its possible to write a driver which runs in a lot less RAM, but it will have worse quality or run much slower and probably both.
“The PC manages it quickly, therefore it must be possible to emulate it quickly”
This doesn't follow. First of all, the hardware is quite different. So for example if the PC can manage fifty times more floating point operations per second then you're going to do most of the heavy weight maths 50x slower than the PC. Or take the CPU cache. The Iyonix for example has only 32kB of cache. So if you've got an algorithm that does random access to 40kB of data (a quite modest size for a LUT in image software), you're thrashing the bus and suddenly the whole CPU is waiting for RAM. On a typical PC that same routine would run from cache, perhaps 10 times faster than the Iyonix even if they were the same CPU speed (and of course the PC will be faster).
But it gets worse - the PC will most likely be running a somewhat modern OS. Even OS X with its laughably naive I/O layer and VM will massively outperform RISC OS. On Linux there are already people trying to optimise for SSDs where there's zero seek delay, finding inefficiencies so small that they were unmeasurable just a few years ago.
“whatever happened to Postscript, TWAIN, etc?”
Postscript is still used at the higher end. It is a full-blown programming language. To run it the printer needs a lot of RAM and a fairly high-end CPU, proportional to the required output resolution (otherwise it will be annoyingly slow). Doing the work in the PC instead thus represents a considerable saving. On a $1500 laser print offering a full Postscript interpreter, including the Adobe license and fonts, is a reasonable decision. On a $100 inkjet printer it isn't going to happen.
TWAIN is the API used to make scanner drivers "drop in" to other applications in Windows and sometimes Mac OS. In the very recent versions of the API there's more thought for other platforms (mainly Linux) but it isn't (as popular idea seems to have it) a platform independent HCI like UVC or EHCI. Each individual "TWAIN compliant" scanner ships with its own OS-specific drivers.