Ichigo always wanted to meet the Shibas. He thought that since Isshin is the previous clan head then by all rights he should be the next one.
He also wanted to do this because he wanted the Shiba clan to be one the great clans of soul society like the Kuchiki. Basically he wanted them to become one of the noble clan again.
He also might want to take Kukaku cause he is a man of culture like us. Also he is currently thinking if he should remove the shinkenger from this world since they are basically cosplayers and don't deserve to have the Shiba name.
No villians and power rangers exist. It is all fake made by them since they wanted popularity and wanted to make people believe they are Shiba descendants which in this world is actually a well respected clan in the history of Japan. They were their samurais and ninjas when Japan went to war.
Now Ichigo went to Urahara and told or more like demand Urahara by blackmailing him with some embarrassing photos that Yoruichi would definitely like as it can be used to embarrass Urahara. Photos so deadly that even the genius Urahara bow down to it.
Once Urahara open the portal, Ichigo shunpo to soul society arriving there as soon as the portal open. He went to the Shiba house which was far away from even Rukongai let alone Sereitei. He knocked on the door.
The guards from the very few Shiba clan told him to stop and asked for his identity. "I am Shiba Ichigo son of clan head Shiba isshin. I have come to take my position and make our clan a noble clan again." Stated Ichigo.
The guard hearing this quickly told Kukaku who was the current clan head and she immediately went to meet Ichigo. To prove Ichigo heritage he showed a picture of him and his dad. Kukaku was mad at her uncle Isshin since she had to take the clan head when she was still young.
Although she may look young, don't let her beautiful and young appearance trick you. She is way older than she looks because soul age way longer than humans. She let him take the clan head position since she doesn't really want it and thought Ichigo was better suited.
Maybe because Ichigo looked like her cousin Shiba Kaien made her decide this. Ichigo quickly order the six people of the Shiba clan excluding his family. There was Ganju, Kukaku and four canon fodders. Ichigo knowing how a clan works made some adjustments and set up trades that would be very successful to make them rich. (I'm not gonna get into details about this since I have no clue myself just think of it as plot armour at its finest sorry 😢)
It won't show now but by the time canon starts, the Shiba clan should be the strongest clan in terms of nobility. Ichigo will make sure no one will take away his family powers. He is not gonna help for nothing like his canon counterpart.
Like seriously the soul society were probably gonna eliminate him if it wasn't for plot like his entire existence is a taboo and if he gets too strong they will deem him a threat. Ichigo will rule them like a proper king and make sure even when there is no soul king the world won't collapse.
Anyone who dares mess with him or try to hurt his family will know his wrath. He will not rule them like a tyrant by all means. He would be fair but very harsh if his family is in danger. He don't care about laws or rules. He makes them not follow them.
This is the Kurosaki Ichigo that is present. Not his canon counterpart or his old self. They merge into one and made this Ichigo. One who is not so selfless to help soul society but is selfless when it comes to his family and friends that he trust. Just wait Yhwach and Aizen your end is coming.