There may not be many places operating the PA38 for those who wish to fly them post-PPL but they do have several advantages over the C152 and even the PA28 Warrior. Advantages are the great all round visibility which encourages good lookout, the extra 5 inches in the cockpit which is helpful if one's student is over 11 stone or wider than 40 inch hips, the extreme simplicity of the controls. Benefit over the PA28 is the fact that I have always felt it was wasteful to carry empty seats around when you are learning to fly so you save fuel and the PA28 has worse visibility. But as someone else points out it does stall properly power off (However, you can get the same effect demonstrating the fully developed stall with flaps and power in a C152) and the spin characteristics are very exciting.
I once heard that the PA38 was designed by a committee trying to ensure that the aircraft exhibited all of the characteristics desirable in a training aeroplane. But isn't something designed by a committee likely to be a camel? However the trimwheel really is unpleasant and the door catches are horrendous...