They only had the WILL to gain power alone or through help of others, it doesn't mean they would automatically gain kage level powers.
With Ashura and Indra he means Senju and Uchiha, or people related to them, not their ghosts, being a reincarnate is all a mental thing, not a physical one, they don't inherit powers through reincarnations only bloodlines.
Only some Uchihas could, not the reincarnates, if reincarnates has all the gifts then this would have been documented, legends would have been known by generations who are better than others, for a thousand years only Madara was known to have gained ems.
MAYBE Madara had some special chakra cus he had the will of Indra but I doubt it. People would have known about certain people being stronger than others systematically in like every generation.
Kushina had special chakra too though.
Look at all those transmigrants, not one of them were known to unlock the secrets of sharingan?
Madara and Hashirama got to where they were cus they lived with survival of the fittest, not cus it was destiny, they walked the paths of Ashura and Indra, clashed like they did cus of Zetsu and all but they didn't get op cus they had the same will.
You must be registered for see images