Ability to use one object to split another

I’m pretty sure this feature isn’t possible at the moment, but please let me know if it is and I’ve overlooked it.
On quite a few occasions I’ve thought it would be useful if objects could be used to split other objects. This would be similar to the current Boolean function where you can subtract/intersect/merge objects, but it would have a few different capabilities and use cases.
Imagine you wanted to create a thin, sharp edged line on the surface of an object like this

At the moment I think the best way to do this is by having a fairly high res mesh and then using the split tool to cut the line into the mesh. However, this can be very time consuming if you need to create a long line, and you might need to cut the line in several stages if it wraps round the back of the object. It can also be tricky to create a thin line of even thickness.
However if we could use objects to split mesh you could snap a tube to the surface where you wanted the line, and then use this new feature to create a split where the surfaces intersect

You could also wrap the tube easily round an object to create split lines that are difficult to do at the moment because of the screenspace/viewpoint dependent nature of splitting with the current tool. (I have tried to make lines like this using the current voxel merge/intersect/subtract functionality, but unless you use insanely high resolution, I find the results aren’t nearly as clean as when splitting)
Of course, creating lines like this is just one potential use case, but I’m sure there could be many others.
Perhaps the underlying math involved would make this difficult - I guess there’s a fundamental difference between how new edges are calculated when doing voxel Boolean split/merge/intersect operations compared to viewpoint dependent booleans like the current split tool uses.
However, if it was possible it would be a really nice feature.

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