Why do LED/OLED HD and UHD displays have "global refresh rates"?
You have to look closely at what type of display device that you have. 

Some displays will only show a picture if you continually scan the video pixel data into the device. These devices do not have a full screen memory to hold a whole image. Instead a separate display controller with access to memory where a screen image is stored will repeatedly read out content of the memory and format it into scan data to feed to the display unit. A typical example of this is the flat screen monitor that you connect to your computer or your laptop screen.

Other devices (many times the smaller form factor displays) will have a display controller built right into the display device. Such controller will either have its own embedded memory for the display image or will use attached memory chip(s). On this type it is possible to address particular pixels or portions of the display to update. The display controller will take care of driving the panel to produce the actual display.

The various flat panel display types are usually run in scan mode to produce a display. Even those that have the built in display controller. This is done for the main factor that it is necessary to drive a panel in a multiplexed matrix manner to reduce the total number of connections between the display controller and the display panel itself. Mostly organized around the idea of rows and columns of pixels. The display depends on the persistence of a pixel to retain its currently visible state from one scan to the next.