Static discharge is nothing more than a difference in the electrical field between 2 items. Scrubbing your socked feet across the carpet builds up the electrical field on your skin. Then you touch the cat, which had a lower surrounding field, and the fields equalize, resulting in the cat getting zapped.
The anti-static band is nothing more than a conduit for the fields to balance between the case and you. Works exactly the same as if you physically touch the case, then pick up a mobo. You equalized the field.
I've been inside pc's since they were first commercially available to the public, built pc's sitting on the carpet of my bedroom, generally clean my good pc doing the same, and never once had static discharge ruin anything.
A pc isn't a Tonka truck, they don't take abuse well, so anything done with your hands inside the case must be done with firm but gentle care. Extending this to mean touching the case frequently is easy. Lean your forearm/elbow on the frame when installing the mobo.
Antistatic bands are really just some enterprising companies way of selling useless items to the safety conscious. Use one if you wish, I don't, many don't, they just tend to be in the way most times.