I'm no expert in recovering capacitors, so can't advice much about this. Some are desoldering and reform the capacitors outside the circuit, others are just powering the entire circuit through a variac, while slightly raising the mains voltage, it depends of the appliance.
I don't really need that 200uF/12V electrolytic from 1981. I've reformed it only only out of curiosity, because when measured was with a MTester it was showing 800uF, way more than it's nominal 200uF.
Increased capacitance is a sign of less aluminium oxide. A thinner layer of oxides also means the max voltage supported become lower than the nominal value printed on the electrolytic capacitor.
Dissolving the oxide layer back into the electrolyte is specific to aluminium electrolytics, I don't think reforming will work for polymer or other type of capacitors, or at least I didn't encounter such reforming other than for Al electrolytics.
As for why wasting time measuring that, no particular reason. I was digging through the scrap boxes, and found an old adjustable supply 0-12V/1A that I've built during the 80's, and was left unused since then. The capacitor after the bridge (another one, a 2200uF/25V from 1982) was hanging in one terminal, so I've desoldered it and measured its capacitance, out of curiosity.
Instead of finding it dried, it was showing slightly more than nominal, and not much leakage, kind of funny. So I've posted that in another thread:
https://www.eevblog.com/forum/chat/rate-my-42-years-old-2200uf25v-electrolitic-capacitor/ 

From one to another, tried a few more long unused 2200uF, and found them slightly different, so I thought it might worth posting the data in this thread instead.
For example, in another box found a 2200uF/16V (the 3rd from the photo, low ESR, 105C, brand OST) with a very strange behavior. Except for the first in the photo, these were scraped from a former AT power supply. Fabricated in 2003, and in use probably until 2005..2010 or so, then scavenged and left unused. This capacitor was showing some "jumps" in current.

First test for 2200uF/16V from 2003, starting with 10V to 20V (maybe starting from 10V was brutal, IDK), 10 minutes each step. It shows a lot of current jumps while the voltage was perfectly steady and constant (and good wires/contacts, I've double checked the jumps were not caused by faulty contacts):

Then, tried again, in the hope that previous measurement also reformed it a little:

Better, but still strange. BTW, looking at the DMM display, those jumps are in fact slow variations, many seconds long. The logging was made at 5 seconds, which make them appear as spikes, but they were more like 1/F noise in reality:
Then I've become curious if the jumps were happening at a lower voltage, too, tried again, this time starting from 0V and going up to 20V:

Turned out the jumps happens at lower voltage, too.

At this point I've decided to let it reform for 5 hours at 16V (its nominal voltage), and this was the measured current during reforming:

And a last run after reforming, still jumpy, but much better then at the first test:

Note that the scale is not the same along the different plots.
For this capacitor I didn't aggregate all the plots together on a single scale, because the big variations will make the other plots look like a flat line. For a closer inspection please find the attached .zip, with the CSV measurements and the .gp Gnuplot scripts to visualize/explore the data at different zooms.