Always.
And here's the big problem with high-density digital devices (like processors, RAM modules and other ESD sensitive devices). There can easily be billions, even 100s of billions of transistor "gates" on a single "chip". This means that each gate is barely larger than the size of a single atom!
That's tiny!
Now the distance a static discharge (arc, spark, microscopic lightning bolt) can jump across a gap, and its destructive power depends entirely on the potential or amount of voltage/static buildup. The higher the voltage, the bigger the spark and the more destructive it can be.
Now here's the bigger problem. The static discharge from our fingertips, can be so huge, it can torch a Grand Canyon size (microscopically speaking), scorched trench through millions of transistor gates, yet still be so tiny, we (as human beings) cannot see, hear or feel that a static discharge has even occurred!
Because destructive electro-static discharges can be so tiny and below "the threshold of human awareness", if anyone says they have never experienced, or destroyed anything with ESD, that simply indicates they don't have an understanding of ESD. The ONLY way to tell if ESD destroyed a device is by direct examination of those gates under a very powerful microscope.
It is wise to be in the habit of touching bare metal of the case interior BEFORE reaching in and frequently thereafter to discharge static in our bodies and to prevent subsequent build up of static. It is important to note just squirming in our clothes can create static. If in that habit, a wristband is not necessary.
When I used to work in a professionally equipped repair facility, we always wore "
quality" wristbands. But I note our benches, floormats, bench mats and the equipment we were working on were always grounded together and to Earth ground too. And those grounding points, and Earth ground itself, were properly and regularly tested and certified - never just assumed.
But most of us don't have such proper repair facilities in our homes. I am in the habit of touching metal, but I never wear a band anymore. IMO - except in professional repair facilities - those bands give a false sense of security and safety. And many are pure junk. Even quality wristbands easily lose their effectiveness as they age and/or get dirty. Sweat, dirt, grime and dead skin is all it takes.
BTW, it is not necessary for the PSU to be plugged into the wall to prevent ESD. All that is needed is for you and the computer to be "at the same ground potential". So even if unplugged from the wall, just touching the bare metal of the case interior will discharge the static in your body and put you and the computer "at the same potential".
This is creating a "floating ground". And that's just fine. Think door knobs, dog's noses, cars, and airplanes. None of them are plugged into the wall.