@XL No i think he's not supposed to and if he attempted black man would probably kill him.
Since it doesn't seem like its something blackman wanted fuushi to know yet.
If the price told him earlier he'd revive everyone because given his nature he'd see it unfair to revive only a few and then he wouldn't have made progress in his training along with not having extra bodies to swap when fighting knockers.
Without any extra bodies, he'd only have inanimate objects and animals and once he gets those stolen he'd turn into a rock and then its gameover.
The ending argument about him not telling fuushi is that the 3 immortals made it appear that they are similar to him being immortal for the sake of keeping his ability a secret because for Fuushi the less skilled warriors he can turn into the weaker he becomes.