Plenty of ways. Teacher takes test for student, teacher re-scores test after student is finsihed, student is placed in an IEP that gives them unlimited time and "reading assistance" for test, failing students are placed in small classes and the class size of average students is expanded, failing students are moved from normal schoolwork to test prep, test questions are leaked/sold (we're talking about a multi-billion dollar industry here, right?).

I didn't make up any of these. This is already happening, and it has nothing to do with positive/negative incentive. It's about test-based education and the natural consequence of trying to control a complex system using a simple metric. It's why education theorists are loathed by teachers--because they swoop in with grand theories of how to fix everything without understanding the system and what is and isn't broken.

It's like an outsider thinking a reasonable way to pay a coder is by how many lines of code they write and how many bugs they fix. Or a civil engineer by how many bridges and roads they produce. Because outsiders don't understand the complexity of the system they think the solution must be simple. Since you seem invested in this idea I suggest you go get some input from teachers and see what they say. My guess is you will learn that the problems with public education is multifactorial and that there isn't a simple fix.