Well, without writing a novel about theory of operation, after departure of OP-Amp U40, the energy is stable expressing little to no spikes. C55 100uf20V should not see more then 19.99xxV. In theory it can run forever at 20V as stated above, and has been tested - This is correct.
However-
Bad quality Caps - If rated voltage of tantalum cap, is too low, if high current applied to the capacitor for a long time, if it is NOT of quality, and the insulation resistance becomes low, they can begin to leak at an increasing rate and with high current, the actual withstand voltage capacity will diminish, effectively halving or more, the voltage rating/capacity. Low quality tantalum capacitors have no real ability above room temperature to actually withstand the rated voltage and when they reach higher temps, the voltage rating will rapidly drop - thermal derating.
IF that isn't the #1 reason they fail/failed, then #2 would be:
High AC ripples. If there is a large enough AC ripple, it CAN and WILL cause a breakdown within the Capacitor even at Voltages well BELOW the cap's rated value. IF the ESR of the cap is not the proper value to deal with AC Ripple, or Ripple is to high, this will occur.
As with most electrolytic caps, the tant cap has polarities.. which generate heat from AC Ripple, which can cause thermal derating / thermal breakdown.
Most people don't know this.
There are no benefits to using AL electrolytic cap, other then the cost effectiveness, easy to find/get, or high capacitance/size. Electrolytic capacitors are just that. The difference remains within the materials used to create it.
Based on real data, If a high quality 20V Tant Cap was used without being exposed to AC Ripple (Properly working Mainframe,Scope,Lines) that had matching ESR characteristics for the tested 50Hz in house power, then it would in fact be ideal for the 501 Power supply.