Concrete cancer can be reduced or even eliminated by using rebar material that rusts more slowly (stainless steel) or not at all (carbon fiber), but these are much more expensive of course. There is room for research on other reinforcing materials, but basically nothing with good tensile strength is going to be cheaper than steel and considering the quantities of rebar we use, cost is definitely a major issue.
The self-healing nature of Roman concrete might also help here, but the chemistry of concrete and rust formation on embedded steel is complex, and without extensive experimentation right now we don't know if steel embedded in Roman concrete rusts faster or more slowly than in modern concrete (before considering cracks).