One expression still is "everything but the kitchen sink", which means all reasonable effort.
But that means the kitchen sink is now the metaphorical "last thing", i.e. the full extent of our effort, the theoretical maximum.
So to "throw the kitchen sink" at something is to put in all your effort, literally everything you've got. (And there's no need for junk in the sink...)
It's a different expression with a different meaning but derived from the first.
And of course metaphors are very often silly... that's why we love using and abusing them! :)