What if instead of mapping positions to 2D points and finding the closest point among 9 samples, you mapped positions to 1D coverage values and picked the maxim

What if instead of mapping positions to 2D points and finding the closest point among 9 samples, you mapped positions to 1D coverage values and picked the maximum value among the 9 samples? Would this make antialiasing easier to implement? What about using 4 samples rather than 9? I'm concerned that the results turn a single point into a square rather than a circle. Would using non-square-grid point distributions alleviate this? Perhaps this could be useful for GPU line rendering, though it's a texture-space algorithm and won't solve drawing a thin line in the first place (which I don't know if it's easier than a thick line or not).