For me this is rather straight forward, capacitors filter voltage for all the components in your system. If the capacitors are aged 20+ years they have often been used long past their lifespan - even if they physically look ok! - they contain a fluid called electrolyte which is a chemical compound that will break down over time and lose its intended properties. When a capacitor goes 'out of spec' it will not do its job properly, causing all sorts of issues with your system: audio glitches, video glitches, stability problems and worse of all - component damage. My advice is - do not risk it, if you truly care about your vintage system, re-cap it!
I will re-cap almost any vintage system, please contact me via the online form or email firstname.lastname@example.org
There are two types of bad caps, ones with visual indicators and ones without. When a capacitor starts to bulge it won't be long until it starts leaking all over your board. This happens because there is an issue with the electrolytic fluid which is a manufacturing defect. The other kind of 'bad cap' is basically just an old capacitor without any manufacturing defects, they won't leak or explode, they just dry up and go out of spec.