Difference between どうにかならない! and 仕方がない when used as an interjection

Question

From what I've been seeing, the two have somewhat similar meanings when used as interjections.

Answer 1

どうにもならない (not どうにかならない) and 仕方がない are similar like you say.

どうにもならない is however reserved for significant things as it conveys irreversibility. E.g. the following is fine:

電気消すの忘れた
仕方がないな

The following is odd because surely it's easy to go back and just switch it off.

電気消すの忘れた
どうにもならないな

The following is thus natural again:

あー、家出る時電気消すの忘れた！もう飛行機あと５分で出るのに
どうにもならないな

Because the situation is irreversible.

Similarly, the following is natural:

ごめん、名札書くときちょっと字汚くなっちゃった
仕方ないな

But the following is almost provocational:

ごめん、書くときちょっと字汚くなっちゃった
どうにもならないな

(Because "Why is this person accusing me of some irreversible mistake, when it just looks slightly bad?")