I have made quite a few press dies out of just mild steel, with the exception of an eye punching die which is H13. So far, there has been no sign of wear other than a little bit of light surface texturing from the scale. I will say however that if you plan on using any sort of tooling in the press, have a hardened die that interacts with the tool or a sacrificial mild steel die that you won't mind getting marred by hard and/or cold tooling (punches, stop blocks, etc.)
John