I believe "on a tear" was mostly used to communicate a sudden violent action rather than continuity e.g. "stock goes on a tear" not because of a steady continuous rise but because it undergoes a sudden violent change of state from flat-lining to vertical. You might be a "tearabout" or a "tearaway" if impetuous, reckless or hard to control.
I can imagine idioms like "tearing up the track" are pleasing in two meanings of the word e.g. that a horse might "tear down the track" in both haste but also in how torn up the track is from their hooves. Same with a speeding car in the days of dirt roads.
However, in modern use, especially about "productive" behaviours, I think it has lost some of the violence and gained more of the continuity sense supported by the pleasing visual imagery of e.g. scissors gliding through wrapping paper.
As a native English speaker I was aware of the older meaning, however as someone that often "quickly explains english" to ESL folk and|or non-Commonwealth English backgrounds I went with "tearing paper" as a starting point as it felt more likely to be familiar.
This is consistent with your last paragraph re: modern usage.
I've got a much thumbed multi volume OED edition on my shelves .. it's boggling how many words have half page or more entries with multiple meanings and historical backstory.
I had hoped it might have come from reading rapidly in the days of uncut pages where you have to eagerly tear each new page to read it. But no, lol.