What is the true reason for the rolling shutter effect on modern CMOS camera?
The reason rolling shutter mode exists is to allow a greater amount of overlap between making the exposure and reading it out. With global shutter, there can be no overlap at all.

For a given technology, the rolling shutter mode gives higher exposure times (i.e., higher sensitivity and SNR) and/or higher frame rates as compared to global shutter mode.

The number of sense amplifiers and ADCs is the same in either case. The cheapest sensors use a single row of sense amplifiers and a single ADC, while higher-end sensors split the sensor array into two halves and have two rows of sense amplifiers and two ADCs.