Firstly, if you get cut, its because you did the technique wrong, not because you didn't run away.
Try and attack Hatsumi Sensei or Stephen Hayes with a sword, and see what unfolds.
Secondly, despite what you may think the katana is a more complicated instrument to use than ''just lunge with it and hope for the best''. A complete amateur fighting with one against even an unarmed expert will have little chance of hurting or killing them, especially if their ukemi is shit hot. Only the top 3 inches or so of the sword blade actually does any damage, and if you miss, you've blown it. Theres actually a specific technique involved in just holding a sword handle, let alone attacking with it. All of which plays a part in the weapon's effectiveness.
Besides which, i can't run because it triggers my asthma. In a combat situation i'd have no choice but to fight.