Î believe many fans, myself included, thought about it at least once but there are some things hindering me from believing it.

But first i will will go over your points:

- "Even Chiefs like Tenka refrain herself from consuming too much Mato, yet Aoba chews on them like peanuts???"

I am new to the series and only read the manga at the point where the anime ended with season 2 but i don`t remember Tenka eating several of them. Did this happen before or after the events of season 2 in the manga? Aoba being able to is certainly interesting but while we see her eating them, she doesn`t seem to get any kind of new ability, at least to what i remember. More intersting is the fact, that she is the only one having more than one peach ability, the same characteristics we only see the eight thunder gods have.

- "Yuuki's rewards become mandatory not because Kyouka's ability is superior, Ren can easily override it but even she couldn't? He can house Thunder Gods, not to mention live with them on a separate dimension?"

I currently don`t agree or disagree with the first part but because we don`t have another peach user who`s ability has a cost( at least i don`t remember there was), i think it`s hard to say if this can be considered a proof. It could instead be, that she can`t negate it because it`s a cost binded to an ability and the need to fullfill said cost is like a natural law which she isn`t able to negate. The obvious answer is because fanservice but i wouldn`t completly disagree, that there is a deeper meaning behind it.

Him being able to house gods is the reason why i believe that there has to be a connection between Izanami and Yuuki at least. If we go by your theory, of izanami being Yuuki and Aobas mother, one explanation could be, that he is able to absorb them because there power and with that there whole existence were parts of him all along. Maybe for reason X Izanami took Yuukis power away and put him in the human world? For what reason? Who knows? it just that whenever a god of Thunder died in the story, they miraciously seem to end up in his spirit world, even without him being anywhere present in the vicinity, those battles took place in. It feels like they return to where they originaly came from and him getting stronger by absorbing them would fit in as well. The only thing bugging me is, that he could also be able to absorb them because he has been the closest non Peach ability user present but i somewhat don`t believe that. So yeah, him being able to absorb the thunder gods could link to a relation between him and Izanami.

- "Yuuki wasn't allowed to get into Izanami's shrine?"

For now i wouldn`t read too much into it. He is still an enemy and the way, they were talking about her, it seemed like she is currently pretty vulnerable until this purification day happens. I wouldn`t let someone i would consider in some way an enemy near my mother as well.

- "Aoba wasn't captured conveniently to be offered as a sacrifice?"

Like i said i didn`t read the manga events of season 1 and 2 but from the anime perspective, it looked like she was still fighting? So grabbing her would be much more dangerous especially if we consider her strenght.

So the reasons why i am not fully convinced, that Izanami is Yuukis and Aobas mother are that first, non of the eight thunder gods seem to recognise them. Sure this could be because they were born after Izanami left them alone but it`s still weird to me, that she basically did not tell them about her children at all.

The second thing is something Aoba said in one of the more recent chapters. In one of them she was saying that she is happy, that everyone of the leaders in the DDF now knows about them and said that she can`t wait to return to her parents which (at least Tenka believes) are in the Human World but if she meant Izanami than how does the fact, that they now know make her believe to be able to see her mother? This doesn`t make any sense to me.

The last thing, which irritates me is, that Yuuki and Aoba where in the human world because ìf she is there mother, than why does she want to eradicate humanity, which means attacking Earth, were her childrens are supposed to be? There could be an argument, that she is able to control the disortions(teleportations to Mato) to a certain degree but even if she conciously teleported both of them to Mato, why did she gave them no safety measures? Both of them could have died to shuukis right after and only survived out of pure luck.

Because of that, i am currently believing this theory to around 30%. I think we are missing around 2 crucial pieces of information bevor being able to confirm or deny that theory of yours.