Why couldn’t Boeing just use the stab trim system to do MCAS job?
No, the 737 NG stabilizer trim system does not feedback from AOA. My source of information comes from this LinkedIn Slide Share and corroborated by this online FCOM.

There are several ways through which the stabilizer can be commanded:


Manually via the trim switches.
Manually via the trim wheels.
Automatically via the Speed Trim System (STS). A helpful explanation of the STS can be found in this answer. STS feeds back from stabilizer position, thrust lever position, airspeed and vertical speed.
Automatically via the Autopilot trim offset. This is only applicable with the relevant autopilot mode engaged.


The Mach Trim function also modifies the trim characteristics. However, it does not actuate the stabilizer and repositions the elevator centering and feel unit instead, which backdrives the column.

MCAS' requirement is completely different from those of the STS or the Mach Trim.