Let’s take a second to consider why it’s unlikely from the get-go. Frequency analysis is not always perfect but it is a valuable tool for assessing the nature of a cryptosystem. By comparing to the expected peaks and valleys, it’s possible to see if it may just be transposition(s) or if a substitution has been employed or if something more complicated is at work. The frequency analysis of K4 shows values that are blunted compared to expected plaintext values. This does not preclude a transpostion or two but it does mean that some method has been used to alter the letters. This basically means that no matter how much you twist and turn the ciphertext, you’ll never find the original plaintext message by transposition alone.
This can be demonstrated even with a double tranposition:
after two keyed-columnar transpositions with Kryptos and Hydra as the respective keywords.
Only using transposition, we’ll never solve K4.–Kryptosfan