If you have a high cost and low cost hash, someone getting the password database can just crack against the low cost hash. Even if the low cost hash is short so

If you have a high cost and low cost hash, someone getting the password database can just crack against the low cost hash. Even if the low cost hash is short so that it frequently returns a false okay (say a nice round number like 1/256 FP rate), you're still reducing the amount of "hard" hashes the attacker has to computer by a factor of that false positive rate.