I have some vintage gear, some of it owned since new, other pieces collected over the years. Most of the gear that I have that is unmodified tests fine, even if they have evidence of small mains leakage or issues that
might be related to aging electrolytic caps. In the cases where it is due to aging components, I normally find a relay is bad, or a ground is compromised. Much less often a bad capacitor. Even when I find a capacitor that is out of spec, it rarely manifests as an issue like blowing up or even just bad sound. A
Mitsubishi preamp I recently tested performs very well, has mains leakage consistent with devices of that era, as well as evidence of additional noise that turned out to be a relay, not a capacitor. The capacitors in it are fine after nearly 50 years. If it did have a bad capacitor, I would need to be careful since it has paper-thin circuit boards, which require care and the right tools and approach to avoid introducing new issues.
Introducing new issues is too common. A friend of mine recently brought over a couple of Yamaha receivers from the '70s. The
CR-1020 the got was unmodified, it needed the controls cleaned, and a rear-panel switch replaced. The controls cleaned up, I wouldn't touch a thing at this point. The CR-2040 had a complete recap and wouldn't power on, unfortunately entirely due to the recap:
As part of the capacitor replacement, the larger capacitors forced whoever modified this to bend the original retaining bracket (middle arrow), which they tried to stabilize with a wedged piece of cardboard instead of a more secure method (top arrow). This caused the supply board to crack when due to the unsupported weight of the larger capacitors (bottom arrow).

This Yamaha is a particularly bad example, but this I see varying degrees of fail in recaps.
I don't personally enjoy much of this rework, so I try to go after the more common issues in my experience, like relays and some of the Si components that do tend to wreck havoc when they degrade. Even if a no-stone-unturned approach might make sense for some enthusiasts, I'm not convinced doing it as a rule is the right approach. So I avoid doing it as a rule. I have vintage stuff, which for the most part I keep as original as possible. I may be erring a bit on that side, but the above CR-2040 above is a bit of a heartbreak that offends my sensibilities more than if it had an original part that aged. I am going to fix this cracked board and traces, so all isn't lost.