Hello RetroTechie,
In what scenario (if any!) would you prefer a small-value electrolytic capacitor over say, a ceramic or tantalum capacitor of similar value / voltage rating.
Such a scenario might be like,
For example, a low ESR capasitor of 0.01uF(ceremic) is connected to a microcontroller's power supply pin and working as power supply decoupling capasitor of that microcontroller. Now to improve circuit board's overall power supply decoupling, we should not put any 1uF ceremic close to the microcontroller. But we can put 1uF electrolytic there.
From intel's application note AP-125("Designing Microcontroller System for Electrically Noisy Environments"), If we look at the paragraph named "Selecting The value of The Decoupling CAP" (page 14) we will see that 1uF(certainly low ESR) will do more harm(transient over/under shoot) than 0.01uF capasitor(certainly low ESR).
Now if we put extra 1uF ceremic, it will get paralleled to 0.01uF ceremic and will do more harm. But if we put 1uF electrolytic it can not be get direct paralleled to 0.01uF ceremic due to electrolytic's higher ESR, and will not form an equivalent 1uF ceremic.
In AP-125's paragraph "Power Supply Distribution and Decoupling" (page 13) it is also said that board decoupler electrolyte capasitors placement in a board is non critical.
AP-125
http://wiki.stei.itb.ac.id/download/attachments/589846/iap125.pdf
Also not why other capacitor types would be better, but the other way around: where/when the common electrolytic type rather than other types, and why?
I saw in national semiconductor's LM2940 (low dropout regulator) datasheet that the output capasitor must have a critical ESR, otherwise the regulator will start to oscillate.
For wide range of temperature, only solid Tantalum capasitor can maintain such ESR. So solid Tantalum capasitors are very important for LDO regulators.