I think there are local variables at work here.
I used a pair of unshielded Cerious ICs for a while. I like their sound a lot, but in my main system switching to them brought a buzz that was pretty audible. My main system has tons of wiring, a cable box, an HT PC, DAC etc., and I live in a downtown location near some radio transmitters. Probably a worse case situation. I wrapped the ICs in copper foil (bought through Amazon) and it reduced the buzz by maybe 80% to a barely acceptable level.
I moved the ICs to my home office system, and the buzz was reduced further -now it was barely audible with the copper foil in place. I've since replaced them with shielded cables, and have no noise issues.
I didn't notice any ill affects from the copper shields, although it was obvious many ICs have much more effective shielding than the copper foil.
Some maintain that lower levels of induced noise is a bad thing and shielding is essential, others believe shielding causes harm. Maybe both are right, in the right application. I also think the signal level, as R Swerdlow has noted, has a real bearing on the audibility of this noise.
In technical applications, such as mixing and mastering, it is always best to keep noise levels as low as possible, but for playback for pleasure, since each installation has its own particulars, trusting you own ears and judgement is a good course.