tl;dr
A stronger, healthier sounding amp; tighter, thumpier, faster low-end tracking; less noise; less ghosting; and keeps the amp from motorboating.
In more detail, filtering does a few things:
1. The preamp is DC powered. The rectifier in a guitar amp converts AC to pulsating DC. A byproduct of this is ripple and noise (120 Hz hum). The main reservoir filter caps charge on the voltage peaks and discharge to the rest of the circuit during the valleys. This smooths the AC ripple riding on the DC supply. So more filtering generally yields lower noise and a smoother DC supply to each gain stage in the preamp. Ghosting typically happens when a note creates harmonic dissonance with this 120 Hz ripple. Reduce the ripple, eliminate the ghosting.
2. Filter caps act as a local energy reserve. Heavy, loud, dynamic playing requires a lot of immediate power to keep the low end tracking fast and tight. When you dig into a heavy chuggy chuggy riff (especially in lower tunings) the power section draws a large current. The rectifier and power transformer can't typically keep up. So filter caps supply the missing power.
3. Filter caps help decouple each gain stage. The B+ line supplies high voltage to each gain stage through a series of dropping resistors. Without filter caps at each of these power supply nodes, the gain stages would share a common impedance path and common filtering. By decoupling each gain stage via dropping resistors and individual filter caps, the caps shunt any stray signal riding on the DC line to ground. Without this filtering, the amplified signal from one stage could modulate and feed back into another stage, causing low-freq. oscillation (motorboating).
In a vintage amp, designed for lower gain rock... this stuff isn't a huge issue. When you start adding more gain and more gain stages and you start playing heavier, faster music, a circuit designed to play classic rock starts to fall apart.
Todd Langner never added individual, decoupled filtering to the extra gain stages in his Marshall mods. At least not that I've seen. And neither do most techs who do mods. When most techs add gain stages, they install another tube and then just wire everything up in series with the existing gain stages. So you end up with FOUR gain stages all sharing common B+ supply node and one 50uF filter cap. This creates all sorts of problems. It's better to install additional filtering for each stage. Takes more time, more work, more effort. But if you're gonna do something, do it right.
This is also why attractive plug-and-play "mods" that you plug into a tube socket only get you so far...