Yes, the metaphor here is that of perhaps a military officer drawing a line and soldiers are expected to stand along the line, so their toes will touch the line

Yes, the metaphor here is that of perhaps a military officer drawing a line and soldiers are expected to stand along the line, so their toes will touch the line. It's about obedience. Early examples are clearly about standing in an orderly formation, and also sometimes use alternative words such as "mark" instead of "line" - which wouldn't make sense for tow. You could tow a line, but it's unclear how one might tow a mark.