Amp is plugged to the wall, why use a conditioner?

There are a lot of GOOD reasons to use a line conditioner. Irrespective of audible effects, a good line conditioner like the Furman products filter a lot of line voltage transients that can damage your equipment. These transients over time can damage sensitive transistors and amplifiers. Not sure if tube equipment is as sensitive, by it only takes a nanosecond transient to destroy solid state devices.

Some products can provide power factor correction, and provide line capacitance that helps the transient response of power amplifiers. I use a Furman Power Factor Pro on all my equipment, particularly the power amps. It reduces line voltage sag when transients hit the power amp. I use another one for the low power stuff like CD players, A/D converters, preamps and the like to isolate them from AC power effects caused by the power amps.

Some line conditioners also can regulate the AC line to smooth out brown outs. I have used the Furman AR-15 which actually has a switched transforment that keeps the output at 110 VAC even if the line drops to 90 VAC or rises to 130 VAC. I have found these can be audible, however, so I only use them on computers and other electronics, not my audio components.

Gdush:

I have one Furman AR-15 for two JC1 mono power amps and a HSU subwoofer; and a second one for the preamp, CD deck, and D/A. The power cords for each AR-15 are connected to the same power outlet. Cannot comment on the products you mention because the AR-15 works differently than all of them (to my knowledge).

In the Furman, the networks (including capacitor storage) are across the ac line, so they do not limit current. Current is limited only by the power cords (and breakers in the extreme).