While you are right in theory - if you knew the load factor and indicated airspeed (IAS) you could determine AoA - how would you measure IAS in practice? Normally a pitot tube would give you incorrect readings at non-zero angles of attack, and that's why airplanes use an input from an AoA sensor for correction. Which brings you back to where you started - an AoA sensor.
You are second-guessing tens (hundreds?) of thousands of engineers who thought about these problems for more than a hundred years.
CL(AoA) = Az.m/(q.A)
(Az = vertical acceleration.) The relationship between coefficient of lift and AoA is a known function that depends on the airfoil. As long as you're below the critical angle of attack, it's an invertible function. (If you're not below the critical AoA, you've already departed controlled flight so it's too late for MCAS.)
This is not true at or near stall conditions.
(If the flight conditions are that unstable, a mechanical AoA vane will struggle too, since it has mechanical inertia.)
It's basic flight physics. The lift developed by the wing is equal to CL.q.A. A is the wing area, the dynamic pressure q is basically indicated by the airspeed indicator, and CL is a known function of AoA. Lift is by definition equal to the load factor * mass.
For a good, in-depth explanation, see http://www.av8n.com/how/htm/aoa.html#sec-ias-aoa