Tool option to act upon centers vs corners

I know people have requested to be able to draw free-hand and based on my reading that’s been controversial and might not happen. Something that would cover some of the use-cases of that for me is if I could draw paths on the screen.

These would be straight lines from the center of one square to the center of another, potentially connected in a chain. It might be implemented as a new option for the edge tool, which already does this with the corner points of the squares instead of the centers. Being able to draw diagonal paths would be nice but not strictly necessary.

I connect this to Drawing Pillars on top of grid points which requests to be able to place tokens on tile corners instead of their centers.

Connecting these ideas as such, we could envision a new setting for multiple tools (token, edge, and measure) selecting whether you want the tool to act upon the centers of the squares or the corners. While the measure & token tools are locked to center points and edge tool is locked to the corner points, these could all be made more flexible by a toggle.