Why such specific resistances in the TL431 datasheet examples?
Because they are using the standard E192 resistor series, which is the required series for the 0.1% tolerance that they specify.

Although some manufacturers may make 22kΩ or 220Ω 0.1% resistors, these are not standard values. For example, 50Ω termination resistors are rather common, but these are not in any E-series.

They might even use 243 (instead of 240 which is in the series) to emphasize the fact that all 3 digits are significant and make sure that readers are paying attention.

The 243Ω divider for the LM317 is due to minimum current requirements of the LM317 itself.