At what distance are balanced XLR cables needed?

I ran a 30-feet Purist Dominus RCA-RCA IC from Aesthetix Callisto Sig line stage to CAT JL-3 amps for a few years and had no problems with noise, radio station pickup, etc. My experience with this one setup nullified many of the theories regularly reported here. You won't know if it a cable works for you unless you try it out yourself.

Atmasphere, whose opinion carries a lot of weight, has suggested that fancy wire is of little value in balanced interconnects.

I value the contributions made here regularly by Atmasphere. But my experiences about balanced and single-ended cable differences significantly differ than his reports here. Once again, don't get too attached to the blanket statements often made here, but rather try many cables for yourself.

IOW if you can hear differences in the cable between the line section and the power amp, then the cable is not being controlled.

Hmmmm, now there's a pretty serious generalization. I have heard significant differences between IC's in the critical line-stage to amp link with Audio Research, CAT, BAT, Aesthetix, Aria/Counterpoint, to name a few products. Are you claiming that the designers of these products are not competent to "control" the cable?

Mariv26: Anything over 3 meters, but I would still keep the interconnects as short as possible

I don't think you can make such a general recommendation

Agreed, as my own experience voids such a generalization.