Those kinds of fans typically use a bronze bushing rather than a bearing. These bushings are long-lived, but eventually wear. When the bearing hole enlarges as part of the wear process, the fan rotor shaft now has additional room for lateral movement in the bearing and can oscillate in the the bearing rapidly, causing the "brrrrr" noise you hear.
You can often extend the life of such bearings by adding a drop of light machine oil to the bearing (usually you have to pull off a sticker on the back of the fan to access the bearing).
I'd imagine the fluid bearing gets a bit worn over time such that it's a bit "looser", i.e. doesn't hold the fan rotor as firmly in a straight/central position.
Not enough movement to sense by hand, and no roughness, but enough looseness / free-play to allow a kind of resonant vibration or "wobble" when the fan is spinning faster.
Edit: or maybe it's just very slightly worn, has debris in the bearing or something, such that it's out-of-round. I think it's the former though (resonance) as that kind of noise can be intermittent.
You can often extend the life of such bearings by adding a drop of light machine oil to the bearing (usually you have to pull off a sticker on the back of the fan to access the bearing).