I have design a number of buildings in Australia on piers (caissons) and without reinforcement but there are a number of things that should be checked:
1. check the codes to see what is the allowable tolerance for the placing of the piers and the placing of the superstructure over. If both of these maximums were to occur at once, then would a plain concrete pier be able to take the eccentricity in bending?
2. What is the slenderness of the pier? if it is less than 3' wide then you may contemplate putting in some steel to allow for slenderness effects. Depending on the type of soil, it may or may not provide restraint against buckling.
3. Is there any later load on the pier? once again will the plain concrete take it in bending?
3. As noted above, what is the soil type, is it expansive,are there any uplift forces on the pier? e.t.c.
If you decide to reinforce it you may not need to reinforce it all the way down - be practical.