I can't think of any good reason to use any of those circuits.
They have a very narrow design margin and are not scalable very far and work only at low frequencies. They integrate but do not dump properly as the switch does not go across the capacitor. Instead, it shuts off the 2nd stage and relies on the passive Rc pullup which also serves as only part of the ramp control.
The traditional way is to use a FET to dump the cap on a true OpAMp Integrator with a discharge time of Tau=Ron* Cfb
Although this is anecdotal, when I started out in design during the 70's I wanted to design a rocket Doppler tracking that gave a linear phase by using the edge of a received 100kHz from an OCXO PLL then used an edge of that zero-crossing signal to sample the phase of a local same frequency 100kHz sawtooth using a sample & hold. So I used a CMOS switch to multiplex between 2 sawtooths 180 deg. apart. so that no Ic=CdV/dt discharge was necessary. It just integrated a squarewave and used the inverted version each half cycle. The rocket motion in range would result in many cycles of Doppler position and the S&H difference frequency signal looked exactly as sharp as the original sawtooth, starting off from a flat line and accelerating up to Mach 7, 500 miles up then re-entering after scanning for aurora plasma dynamic properties. The slope of the resulting triangle change slopes as it counted down back to earth and the distance away for recovery was cycles converted to distance. Two antennae with a time-interval counter gave azimuth after signal processing.