Why are the total energies of transition states so commonly corrected for zero-point vibrational energy?
At the transition state, you have exactly one vibration mode with imaginary frequency (which corresponds locally to the reaction coordinate), and $3N-1$ other “normal” vibration modes. In the transition state theory, you separate out the reaction coordinate (consider it infinitely slow compared to the other movements). Thus, when you consider the energy of the transition state, you have to include the contributions of ground state energy of all the other vibration modes.

The more rigorous way of looking at it is to use statistical physics, and to consider the partition function of the transition state. See here or there for such treatments.