They use it as input to A2D converters. You can get your Ph. D, in Sample and hold circuit design. Sometimes people would concentrate on architecture and design of A2D (SAR, Pipeline, flash, sigma delta, etc..) and use good sample an hold chip from external source, or buy the IP and put it on their chip. Also, there are event driven experiments and data collection that may need sample and hold circuit only. You can use another Analog Circuit instead of A2D to do something, for example you can subtract output voltage of Sample and Hold from reference voltage to adjust speed of DC Motor or light. You probably could replace phase detector of PLL loop with this contraption. You can square this difference or do another mathematical manipulation to generate control signal. Anyways there is another tool in your tool box, or another Lego block for your creation.
Sometimes those pins on the capacitor storage, are on teflon standoffs as the leakage of pcb, affects the resistance (10^18 is a big resistor value).. Even humidity can affect the value.. And flux is a big no-no
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