The ADCs the photo sensors use are "ramp-compare" type. Which means that in order to evaluate one 13-bit pixel the ADC needs to pass through 2¹³ = 8192 cycles. For a 14-bit pixel, the number of cycles (and thus the time) per pixel doubles.
For the electronic shutter, the rolling shutter effect is determined by the speed of pixel processing (accessing, analog-to-digital conversion, digital throughput). If analog-to-digital conversion is the bottleneck, it is possible to increase its speed by a factor of two or four by dropping one or two bits of its resolution (by doubling or quadrupling the magnitude of the ramp-up step of the ADC).
For the fully mechanical shutter and the EFCS, the rolling shutter effect is determined by the speed of the mechnical shutter, and then the sensor readout could be continued when the sensor is covered by the mechanical shutter. However, you still need to read the whole sensor before you can start a new exposure. So, to increase your frame rate with EFCS, you may also want to decrease the bitness of your ADC.
For the "natural" (limited by the photon physics) dynamic range of a sensor with Bayer pattern and a pixel pitch of R5 at ISO 800 and above, 12 bits of the value representation are enough, and you don't need an ADC with a higher bitness. Lower ISOs mean potentially more photons per pixel cell and more bits to be useful for recording the full DR.