It's one of those stories that zing around and will never die.
The "all magic" cap-kit story. I was in the arcade collecting circuit for about 10 years and whenever people posted a problem with any electronics there were always loads of people saying cap-kit, cap-kit....
Very often, very very often, the cap-kit bought was of cheap Chinese modern caps.....or sometimes they used NOS caps that had been laying in racks for 30+ years.
Both result in a much WORSE situation.
Cheap Chinese caps....don't.
30+ year old caps......are usually worse than those who are of the same age but have been in use regularly. Electrolytic caps need "exercise".
I've worked on loads of monitors, arcade PCBs and sure...I found bad caps. And yes I replaced those, with GOOD quality new ones. I mostly used Panasonic and sometimes Nichicon, low ESR, 105 degree caps.
Caps that go kaputt are usually small in size AND have endured heat for long periods of time.
Ever since I bought a good ESR meter I've only measured all caps on my devices. Usually, they are all fine.
Even though the brands of caps I've found in Atari homecomputers aren't a well known brand (Atari arcade only used Nichicons) I have yet to find a bad one...the lack of heat inside A8's is one of the reasons for this.
I own a 1971 Seeburg jukebox. It has all caps of two brands: Sprague and Siemens. I have measure them all. NONE were bad, actually, they all showed specs well over there indicated capacitance and low ESR values.
I HAVE found leaking caps in Atari Lynxes though (definitly check those, I only noticed the leak after removing a cap). And I have some doubts about the caps in my Mega STE PSU...they seem to be "just" in spec.
I also recently bought a early 90's midi-module (Korg). It showed NO output on both Jack terminals and very low output on the 3.5mm connector, the left channel being slightly better than the right one, but even with my amp fully cranked up, the volume was very low. So I got out my ESR meter and started testing the SMD caps. About ALL of them were defective. To my amazement some even showed "infinite" ESR values....which explained why there was no sound on the jack terminals.
I replaced them all (my first ever SMD cap job) and now it rund 100% again. To be honest, the Korg doesn't get hot inside, but I read that early 90's SMD caps are known to be bad...
Anyway....the story is that there is never one solution to this. And you have to decide for your own.... I personally check the A8 caps visually and with my meter and then leave them.