Yes, very pertinent point. Do you know if the mainboard connections are the same still? Or have they been changed since this psu was new? It'd be a shame to retire the psu in my oppinion.
Power supplies have perishable components in them, one of which are multiple electrolytic capacitors. These age over time but not like fine wine. Their ability to hold a charge becomes compromised and eventually they will leak fluid.
12 volt regulation circuitry can go out of spec along with weakening ripple suppression and damage other system components slowly even though the power supply seems to be working fine. This has the effect of shortening the lifespan of other parts.
Protective circuitry can also lose effectiveness over time and if the power supply fails, it can take the system down with it. This would be a hard lesson to learn with a bunch of new components getting fried. Modern power supplies include better protections than older models and are in fact a safety device besides delivering system power.
Motherboard connections are largely unchanged in the last 10 years or so. If your power supply has a 24-pin main connection, EPS 4+4 (CPU), SATA (disk drives) and PCIe (video card) connectors then it's fine, as far as connectors are concerned.
A new power supply will come with all the cables you need for new system components. A high quality model will come with a 7-10 year warranty and is a great investment for system reliability and dependability. Take it from an old gamer himself (Doom, Quake, Earthsiege II, Mechwarrior 2).