Timlub, Things that look simple not always are. There is no such thing as "Linear Power Supply", unless Linear means "Unregulated". In reality it is primitive unregulated switcher that operates at 120Hz and switches at max voltage. Current from mains is delivered to capacitors in very narrow current spikes of very high amplitude. Amplitude of these current spikes depends on transformer, power cable, ESR of capacitor etc. while width of the spikes depends on the ripple amount that, in turn, depends on the load current (definition of the switcher). In addition to current spikes charging capacitors you get also very narrow spikes at the peak of the (rectified sine wave) voltage when rectifier starts conducting for a moment in opposite direction to quickly snap back. To widen this spike there are "soft" diodes (like HexFET), that conduct fast but snap back slow. I'm trying to show that operation of such primitive supply is not as simple as it seems and the fact that larger cap works means only that safety margin for rectifiers still exists but was reduced and might be very small. If we believe that designer put unnecessary margin by mistake that's OK, but I would ask him :)
As for inductance - electrolytic caps are inductive. Inductance of such cap is proportional to capacitance. Increase in capacitance means increase in inductance. Believe it or not, but power supply caps are in series with your speaker (circuit is closing thru them) and their inductance can affect response time.