It's a theory I said earlier. I'm pretty sure that to have a successful birth of the otherworlder, a mother needs to be particularly powerful. All the death traps could simply carry the logic of: if Lilia can't even get past this shit, she is clearly not worthy. In fact it very much seems like they only become worthy when their magic is at their peek, the purification ritual fully charged. If you lose the otherworlder fight early, you still only become a nanny to an abomination broodling. It seems like it takes imense magic to be able to properly host the otherworlder.
Also, it can also be simple information asymmetry. The minions of the Father don't know exactly what is needed to get him birthed into this world. That's why they took away pregnant woman to experiment on them. They are just throwing shit at the wall to see what sticks. Plus half of them went crazy anyway experimenting with other stuff, like expanding their minds that got them mind blown and turned into half corporeal brain slugs.
The minions of the Father are not a solid unit, they are not well coordinated and managed, they are a bunch of crazy fanatics and corrupted monsters fumbling over themselves each having their own stupid inaccurate interpretation of how to serve their master.
Even the demihumans for example are servants of the Father btw. Look at the masks the high ranking ones wear with the white face and central eye like design. Looks like the central slit on the face of the Father. However the deihumans probably don't even understand it, the worship the demihuman god cause they can see that clearly, and the father, being the master of the demihuman god, they can just kinda feel it in their soul, whispering in the back of their head. They get the urge to rape and impregnate but don't understand why. They make the woman they impregnated wear a mask and they paint the eye on the pregnant belly too. They are trying to please their unseen master, they just have absolutely no idea what the fuck they are doing and are clearly failing at their jobs.
The father probably can't properly communicate to his servants, his language way beyond mortal understanding. At best he can convey ideas or feelings to his servants, all the while his mere presence corrupts and drives them crazy.