I'm not sure where you are going with this question. If you delete vertices, the whole transition between keyframes will be fouled up. If you have the wrong keyframe interpolation set up, you can get weird bounces between keyframes. This applies to vector paths, motion paths, and even color or opacity keyframes.
I haven't fiddled with an expression to look for vertices that don't change position between keyframes, but any expression that looks back at a position value for every vertex in a complex shape or mask path and then compares that with the position of every other vertex or point in the path is going to be very slow. Expressions don't remember what happened before the current frame; they have to look back one frame, then one more, then back again until they get to the start of the timeline. They become recursive and will slow down your render. I'm not as much of an expression expert as Dan Ebberts, but It would not surprise me that an expression that looks at a path with hundreds of points and tries to figure out which ones did not change position would slow down to a complete crawl in just a few frames. As far as I know, the only way to get the position of a path point is to implement the language generated by the Create Nulls from Paths script in the window menu. A path with 100 points would generate 100 null layers or require at least 100 look back lines of code for every vertex. Dan would know for sure, but I am pretty sure that this would be an insanely difficult and inefficient way to approach your workflow problem.
I have done hundreds of complex animated maps and chart illustrations with complex animated shapes and mask paths. I usually use Rotobezier paths instead of standard vertex paths because there are fewer handles to fiddle with. When I do that moving line animation, I almost always apply "Create Nulls from Paths/Points Follow Nulls" from the path at its most complicated shape. Then, I manually add position keyframes to the nulls. It usually does not take very many keyframes, and it's pretty easy to move the nulls around and even use parenting to simplify the animation workflow. I set up the keyframe interpolation methods to be linear. If I need to finess the timing, I pre-compose and apply time remapping instead of messing with easing or the Graph Editor on all those keyframed properties.
I hope this long-winded explanation helps you figure out an easier way to animate your battle lines.
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