In Blender 2.9 (and I think also 2.8), you can parent a whole object to a specific bone, but it's not particularly straight forward.

How-to

1. In Object mode, select first the object you want to parent, then the armature that the bone belongs to (shift-LMB).
2. Change to Pose mode, and select the specific bone you want to parent to.
3. Press Ctrl-P to open the parenting menu, and choose Bone.

Done!

My use case

I had a model consisting of two objects (something like a head and a hat). I wanted to animate them both (for example the head turning to the side, while the hat goes up and down). This can be done directly in Blender, by animating their individual transforms. But my problem was that I wanted to have multiple animations for this model, and export that to Unity as a single FBX. In Blender, animating separate objects doesn't allow you to do that (AFAIK), because it creates separate actions for each object, which get then all exported individually to Unity.

My solution (a bit convoluted, I'm still researching this) was to create a standalone armature with two bones, and assign each object to one of the bones. Then I could animate the armature, and a single action could control both objects. Step 2 tripped me for a while...