Sounds like it's a thought-terminating cliche- of which we have many in English.

Maybe that negation would be too obviously related to the idiom. There are other ways to say there is a way; e.g. instead of shikata, there is houhou： 方法　（方法がある）.

The counter-idiom, if you will, to "nothing can be done" might be "where there is a will, there is a way":

意志のあるところには方法がある。

If someone says しょうがない　or しかたがない, and you don't agree, that might be the thing.

That's educational. Had a boss who normally on an even keel then someone said "it is what it is" to him and he got very, very angry. It was like someone kicked him. He said that was just unacceptable and we would find a solution / work around. I guess I now know the other half of the story.