The main reason the plasma needs to be kept away from the walls is that they will conduct the heat away from the plasma and the hot gas will cease being a plasm

The main reason the plasma needs to be kept away from the walls is that they will conduct the heat away from the plasma and the hot gas will cease being a plasma. It has analogies with static electricity. Static electricity might have a voltage of tens of thousands of volts, but it does little damage when you touch someone as the number of electrons (current) is so small that not much energy is involved. Similarly with a plasma. The temperature (energy per particle) is very high but the number of particles is small, so the total energy is low. Touching something will cause the energy to leak away (cf. static electricity discharge) converting the hot plasma back to cool gas.