Reason for asymmetry?

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Why is the right side of images made with analog video synthesizers often more heavily modulated?

What the curtain does would be a good example of what I mean. The shadow is always on the right side of the edge. But also when adding modulation in other cases, the right side of the image is always more affected by it than the left side.

I can imagine that since the image is built up from left to right, any mathematical operation on the signal can only affect the part of the signal that comes next, which is on the right side.

But if that is the case I would think the effect could also be applied to the lower part of the image. So, for instance, why isn’t it possible to have the shadow the Curtain produces beneath the edge in stead of on the right? Is that not possible because of how it works or is that a design choice?

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If I’m understanding what you are asking, a ramp will be at 0v at the left of the screen, going up to 1v at the right of the screen.
If the ramp is the input for the amount of modulation, that amount will increase towards the right of the screen, because the voltage (amount of modulation) is increasing towards the right. This gives a more pronounced effect at the right.

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If you put the range switch into the left position, it will blur downwards.

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But, yeah, I think your description of why is accurate — because the signal is itself linear, moving left to right and top to bottom.