Concept and execution are fine.
Yes, this is a situation where throwing away KK would be a viable, even correct option. First to act + limpers/limp-callers + paired paint on board = bad. More than likely you are beat, and would probably have to spend alot of your stack to find that out. Aside from catching the two-out K on the following two streets (maybe one out if an opponent is holding KQ in which case you will win the stack, but outside that .....) you are likely dead in the water, especially if anyone else calls that min-bet.
In this example, if raised, fold it, if called, shut it down and not put another dime into that pot.