1st Bold: i understand what you meant by having both makes you closer, this same logic can apply to Izanagi, having the DNA makes it complete(or close to complete), not having the DNA makes it incomplete but still usable which ties back to using the DNA to prolong it's effect. Izanagi is named a kinjutsu because of the short usage of this skill, if the skill is not used at the right time, Izanagi won't be able to protect the user.
2nd Bold: Izanami is an example of altering reality yet it requires only Sharingan/Uchiha Bloodline.
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Here as you can see it says "Those who
couldn't control Hashirama's Powers (DNA) boasted only an Incomplete form of Izanagi"
We can keep arguing about this all day the Manga contradicts itself just leave it at that.
What Tobi said in that page doesn't contradict the statement (from three different sources) he made about Izanagi's requirements.
What we got overall was:
> Izanagi can only be used by those with Uchiha and Senju powers.
> Those who couldn't completely control Hashirama (a particular Senju whose chakra is especially hard to tame) could use Izanagi - they met the minimum requirements - but it wasn't complete because of their control.
It doesn't discredit the idea that you do need Senju powers alongside Uchiha powers to 'unlock' the ability to use Izanagi.
Izanagi changes destiny; it turns illusion into reality. Though it only affects the caster, the effects are 'real'.
Izanami doesn't alter reality per se.
Izanami decides destiny; it turns reality into illusion. It affects the opponent, and the effects aren't real. The looped illusion however seems to contain things which can happen in reality.
In context: Izanami can only decide destiny by forcing the victim to accept the consequences of their actions, and their true selves. In the case with Izanagi users it forces them to accept a result they avoided was out of their control before releasing them.
Itachi's summaries make sense, however it doesn't necessarily suggest that Izanami controls reality on the scale Izanagi does.
Another way of looking at it is: power hungry Uchiha, who'd kill their rivals for the power to alter reality, use Izanagi. Uchiha who weren't power hungry - thus didn't take Senju DNA - devised Izanami to force their brethren to accept the actual reality, not the 're-done' reality.
In this sense, it makes perfect sense as to why Izanagi requires Senju powers alongside Uchiha and why Izanami doesn't.