You may be assuming too much from this circuit. It may not be equivalent to a high voltage tester, and the results from using this tester may not tell you about high voltage failure modes.
Now I haven't looked at the actual circuit, and I haven't seen Mr Carlson's video on how it is designed, so I am basing everything on observation of him using the tester.
But what it looks like from the outside is that the circuit charges up the test capacitor and then tests to see if it maintains voltage under charge. If the capacitor holds the voltage it is good. If the capacitor does not hold its voltage when charged then it leaks. This can be made to drive a display.
Let's say we wanted to design a circuit around this idea. One way we could do that is to charge up two capacitors side by side. One is a known good capacitor and one is the capacitor under test. After they are charged, compare their voltages using a differential amplifier. If the voltages remain the same, the test capacitor is good. But if the test capacitor leaks its voltage will decline and the differential amplifier will see a voltage difference. This difference can be used to drive the bar graph on the display.
I've no idea if Mr Carlson's tester actually works this way, but it is one way I can think of to replicate the function of his device.