There are plenty of good reasons you might need a line that's visible regardless of the dimensions. Here's a screenshot from a game I made where you're able to zoom in and out:
You can see red lines that represent lasers, and blue circles that represent shields. Most of the graphical elements resize when you zoom in and out, but the thickness of the lines and the circles do not, even though the endpoints of the lines and the center and radius of the circles scale appropriately. This is what I wanted when I made the game. I didn't want lasers that become invisible when you zoom out. I don't care if it's "unrealistic" in whatever sense. It's more important that they be visible to the player than that they be properly scaled in thickness.
Another example off the top of my head is pathfinding. If you give orders to a unit to move from one point to another, and you want to highlight the path that unit is going to take, that's not an in-game object, that's a marker for the player, and it needs to be visible to the player even if you're zoomed out. If you draw it with lines, you want those lines to be visible.
If you're familiar with OpenGL, which fully supports the scaling mechanism you desire, this is exactly what you get when you call glBegin(GL_LINES): lines of 1 pixel in thickness, regardless of your scale. When you specify glLineWidth, you specify it in *pixels*, not in unscaled units. Similarly with GL_POINTS: you get points of 1 pixel, regardless of scale.
About (b): maybe I am missing the point as it seems obvious to me that
> consider the filled, closed polygon from (10, 99.6) to (90, 99.6) to (50,
> 200). Would drawing that cause any pixels on the 100x100 screen to be
> lit up or not?
it shouldn't. Unless you want to do something like smoothscale does (and
thus using intensity as a mean to simulate fractions of a pixel) all the
points, once scaled, are outside the surface... did I misunderstand