Adding filter caps to the power circuit is easier and cheaper than adding more inductors. Filter caps usually come in two flavors. The caps in Marshalls actually contain two or more capacitors in one container. Filter caps can be added before or after the inductor in the circuit. This combination of using the center tapped transformer, the rectifiers, the inductor, and the filter caps results in a relatively constant power flow through the amplifier.
Electrolytic capacitors have a finite lifetime, usually about ten years.
When they get old, filter caps can lose some storage capacity, which will result in a rougher power flow, possibly leading to hum in the amp. The filter caps may also short out internally, allowing the power to flow directly to ground which results in blown fuses. The rectifier tube in your amp plays an important part in its sonic character. I've experimented with several rectifiers and have been convinced of this. While some amps will not exhibit much of a difference in sound between rectifiers, others can be quite dramatic.