I think a reason why none of Void consider that possibility is because I think any logical thinking was thrown out the window because they were scared of losing their Divine Luck or due to how traumatizing their past is; they didn't think clearly.
As say, trauma can make you do some really stupid things so I think that could be why none of them thought that and I think that's what I'm doing in DTFA; that even the most logical members like Hajime and Emma are acting based on trauma, especially as compare to Hajime and Emma, they got their Divine Luck at an even younger age then those like Nikei and Iroha which could explain why they went along with this plan. - Mod Poi
That is probably the only way it could work, that they are so scared and desperate that they just acted on the first thing they think could work without having to think and go "Hang on a moment, this is actually really stupid."
Heck you already get this foreshadowing in Chapter 4 when Nikei is telling the story of Void's origins, because while I do think he was massively downplaying how horrible of a leader he was before Mikado, the fact the others all decided to go with Mikado's plans is a sign of how desperate they were. Any thoughts if it could be too good to be true don't mean much if you got nothing to lose.
It also doesn't help that with Koroko being a expert psychologist and Mikado being created by her, he has a complete understanding of the human mind, so he knows exactly what to do to break and manipulate the Voids into going along with his plans.
I can't wait that when the SDRA2 events blow over in DTFA and the Anons have finished chewing out Void for their forced assistance, Nagi then gives them a heck of a lecture on why they are all dumbarses who were doomed to fail.
