What specific evidence is there for P = RP?
The existence of problems in DTIME(2^O(n)) which require exponential-size circuits to compute (which is the assumption in IW) seems plausible since otherwise we would have non-uniformity giving a speedup on EVERY computational problem -- which goes completely against the current thinking that does not see a "too significant" gap between uniform and non-uniform complexity for "normal" problems.  This thinking comes from the fact that there are very few examples where a "non-uniform" algorithm is known that is significantly better than the known uniform one (again except for derandomization).

Another piece of "evidence" is that relative to a random oracle we do have P=BPP.