Okay, well I actually do Iaijutsu and have done tamashigiri on many occasions, and I can say from personal experience that the "Strength does not help" dogma is bunk. Especially because fighting is not cutting an immobile piece of mat.

First off... immobile piece of mat. Big guys cutting tatami aren't thrusting either which is definitely a valid tactic. Second, while using katana to cut tatami is a skill based exercise, strength does not mean that there is no skill. It's big fallacy people seem to get into. Strength <> Lack of skill. A stronger sword user can use a heavier sword. You know, because similar weapons do not mean they are the same.

A heavier sword with more power to wield it, can cut easier, especially larger targets, than a smaller one can.

If you think strength doesn't matter, duck tape a katana to a hippopotamas. then piss it off and fight it. It has no skill but plenty of strength and I'd bet 10-1 you'd die before it did.