I guess we can presume Orsted healed Rudeus because so far Rudeus is the only lead to Hitogami. Rudeus is weak from Orsted's point of view, so Rudeus himself wouldn't be any great danger. That's why leaving Rudeus alive might grant Orsted a chance to track down Hitogami himself. Killing Rudeus could be a small inconvenience to Hitogami's plans, but on the other hand it would send Orsted back to square one.