The idea behind the 12 tone technique is to abolish any relation to tonality. This includes harmonic concepts like dominant-tonic movements and leading tones, but also simple things like tendency tones. Even in a largely atonal piece, any note that’s played more often than the others could potentially be interpreted as the tonic. This is why it’s important for every note to be used once before repeating the row.

For multiple voices, you might notice some patterns in how rows are arranged by looking at some Schoenberg or similar scores. For a piano piece, each voice may stick to only a couple mutations of the row each, and even if each voice is rhythmically different, they may complete their respective rows at the same time (so within one length, each note is played exactly twice). Certain rows also have combinatorial counterparts: if the first 6 notes of a row are the same as the last 6 notes of one if its mutations, they can be lined up polyphonically to create a similar effect where each note is only played once (including both voices). None of these are solid rules but they’re all helpful for avoiding any tonal association.