Why did my old PC perform acceptability on 1/8th the RAM doing all the things you say use "extra overhead" ?
There hasn't been a desktop OS that ran in 16M for years. There used to be and they did many of the things modern OSes do but how is that relevant?
And who says it has to be a background service ? Just foreground it for older devices.
It's not about the RAM for one particular task. Modern software is built on modular frameworks. It's the only way to get reasonable development efficiency and stability. With frameworks, you get it all or you get none.
Printing, as implemented in iOS probably depends on the multitasking frameworks, the notification frameworks, the dock frameworks, interapplication communication frameworks, and so on. So the hardware requirement is actually the requirement to load and use ALL those frameworks. If the hardware can't support them all, then, sure, Apple could implement printing using some other method but that becomes a one-off development task for one feature to support a small subset of the user base. The software engineering cost of that kind of thing is very high and, apparently, Apple has decided it isn't worth paying it.