Go into weight paint mode to see the influence your vertex group has on your mesh. In this case it looks like your mesh doesn’t have enough geometry for it to do what you want it to.
It happens because blender store these faces as “vertex groups”. And that’s how blender vertex selection works, you can’t do anything about it sadly. Blender can’t store edge or face selections. If you select these faces and switch to vertex selection in edit mode you will understand what’s happening when you’re trying to store them as “vertex groups”. Blender selection method just won’t allow you this.
Good news: the ambiguity inherent in VERTEX GROUPS for Faces has been solved by the advent of “FACE MAPS” (why why why “Maps” instead of “Groups” to be consistent??? )
Same tab as VERTEX GROUPS, a bit further down.
Celebrate!
(Why they didn’t take the next logical step and throw in EDGE GROUPS, ala C4D, I don’t know.)
EG: this selection is not storable in Vertex Groups, but is in Face () Maps.
Because they are not the same thing. And made for completely different purpose. They were made for rigging and animation. You can’t store the same faces in different maps as well, but you can with “vertex groups” and you can’t plug face maps in anything (modifiers etc)
Obviously if your intent to just store them as “selections” to re-select them later you can do that i guess. But you can’t do anything else with them, that’s why they called “maps” and not “groups” they are just not the same thing.