The option has a support condition
Apple says the external-display Refresh rate option appears when a connected display supports changing it. If the menu is absent, identify the selected display and the actual connection route before assuming the video app removed a control.
A laptop panel, external monitor and television can expose different choices. Make sure Displays settings is focused on the intended external screen.
Check the whole mode combination
Review the Mac model, cable or adapter and display specification together. A television’s maximum rate does not prove that every adapter or multi-display arrangement can carry it at the desired resolution.
If a dock is involved, use Apple’s documented direct-connection comparison where practical. Keep the TV and source fixed so the changed route is the main variable.
Questions answered
Should every connected TV expose a refresh selector?
Apple makes availability dependent on supported external-display behavior.
Does a connector shape prove the available rate?
No. The complete hardware and mode combination matters.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.

