Some things will hum if the shields are off, especially phono preamps.
Anything that came with shields keeps them, and occasionally I've added them. Some things are a bit on the fussy side and you can measure hum or cross-talk from the tube being unshielded. Something I picked up from Dave, my Pilot SA-260 has a very measurable amount of channel to channel cross-talk that almost completely goes away with a shield over the voltage amp tube. The small tube being next to the output tubes gets some signal bleed. I won't tell you I can hear that, but its easy to measure and at some point when I feel ambitious I'll swap that socket out for a shielded one to fix it.