When describing the colour of light globes, you see temperatures like 2700 K or 6000 K. The surface of the sun is around 5500 K. This could be written as 2.7 kilo-Kelvin or 2.7 kK (or 6 kK, 5.5 kK respectively), but is this avoided for clarity?
In certain fields there are "customary" ways of managing unit multipliers. For thousands of kelvins, they are expressed as four-digit or 5-digit numbers. Similarly, for measurements of small mechanical parts, decimal inches almost always are given with three digits to the right of the decimal point.
The SI multiples of the kelvin are used in the scientific literature, kilokelvin and kK included. This is a fact, and it is easily verifiable with a quick search using Google Scholar. It is also a fact that its frequency is smaller than, say, kilojoule. However I think this is understandable, by taking into account that kK are typical temperatures in Astrophysics, while typical energy scales of macroscopic matter under normal conditions are expressed in kilojoule per mole.