I'm sure there are times when replacing electrolytic caps helps a situation in an electronic circuit.
I am a maintenance/reliability engineer by profession. I graduated from the Naval Academy in '84, minored in electrical engineering, majored in mechanical. Living near OC Maryland, I know that you know where that is. I design and specify both electrical/mechanical/electronic equipment and machinery, and write manuals and procedures on how best to keep the equipment running efficiently and economically.
First, let me say there is a wealth of knowledge on this site. Lots of great factual information and resources, and folks who really know their stuff about spinning vinyl, the mechanics/physics/results. When I was in "college", all I really knew was that most of the equipment was out of my price range. I had a simple NAD 5025 TT and the NAD 9200 cartridge. I had the Sherwood receiver, my roommate had the Boston Acoustics speakers and Tecnics DBX cassette deck. Enjoyed my/our music. After all these years, and exploring my inherited vinyl collection, I have a renewed interest in playing vinyl as do so many on this site.
Back to capacitors. Electrolytic caps are notoriously non-precise devices when brand new. +/- 20%, or more, tolerance from nominal value is normal. They are used in the circuits where large size (capacitance) and tolerance is not an issue, such as in power supplies. They are used for filters, mostly, an applications where exact value doesn't matter. They are SELDOM used in any critical signal path. Standard electrolytics are made from an aluminum can (outer) and spiral-wound foil sheets separated by (in many cases) waxed paper or plastic film. A non-corrosive electrolytic paste is used on the insulator between the aluminum sheets. So, the electrolyte paste does not lose its "capacitance".
In almost any use of electrolytics, look at any circuit board, (especially pre-1992), and the use of an electrolytic cap means there is a power supply section present; either main supply or sub-supply (bias circuit for example). I have dealt with many circuit failures over the last 33 years, in military aircraft avionics to industrial equipment; electrolytic cap failure is not the first place I look for root cause on a circuit board or system. Probing with an O'scope or meter and looking for voltage (or lack of)is far easier than replacing perfectly good caps. Usually diode failure or resister failure is the root symptom; root cause is badly spec'ed diodes or resistors (not spec'd for enough heat dissipation).
I think treating electrolytic caps as a precision device is foolhardy. Much faster just to probe the voltage from the power supply and look for deviations there. Shoot, if anyone is going to replace caps at a glance, in order to "improve" their device or equipment due its age, go ahead and replace the rectifier diodes too! And where do we stop? Start replacing worn out transistors while we're at it, why don't we?
Part of the love of playing vinyl is that it is very "hands on". Lots of satisfaction to be had from choosing equipment, setting it up, alignment, interconnects, cleaning, etc. Lots of subjective stuff to do.
But replacing capacitors as a "norm" on vintage equipment just doesn't work for me, until I have proven they are bad. And in all my years, and equipment over 90 years old, I haven't witnessed the justification for replacing electrolytic caps just because they are "there".
Often....invention is the mother of necessity.