The actual antenna is always balanced (as there are no magnetic monopoles in nature at any frequency, including RF). However, the actual antenna may include stuff that most people do not normally include in what they call "the antenna". And the balance may or may not have geometric symmetry.
This stuff is many, such as, with a handheld HT, ones hand, arm, and body. Or in a typical HF setup, the feedline, mast, guy wires, radio case, transmitter power feed, ground lines, computer network cables, household wiring, gutters, metal fences, trees, salt water/moisture, and etc. All of which can end up with accelerated current flow from the transmitted RF field or feed, and thus affect the RF radiation pattern, even if completely disconnected, but still reasonably close to the RF near-field (such as with electrically isolated Yagi-Uda director and reflector elements).
In the case of a VHF HT, the operator's body being part of the antenna system may actually be an advantage. Same with the feedline when operating an end-fed antenna SOTA QRP. But in the case of HF at higher power levels, touching the case of a transmitter (etc.) connected to an unbalanced feedline located at an SWR peak may cause unpleasant surprises.
For safety, an operator might want to minimize these unpleasant surprises in those parts of the antenna that are not called "the antenna". For communication efficiency, one might not want those parts of the antenna other than what one calls the antenna to distort the expected radiation pattern and aim it in useless directions, such as directly into the dirt, or sideways from the desired target.
Radials, or a solid ground plane, are one mechanism to aid in reflecting the antenna's RF pattern back up out of the dirt, and more into more useful directions. But even directly into the dirt might be more pleasant (and safe!) than though your body into the dirt. Thus safety grounds.
But sometimes, grounding a portion of the (named) antenna just makes the antenna modeling (completely correct math with mostly bogus assumptions) easier.