Aldrich couldn't take any risk.
He already could not use his Perception, and even if he could, he couldn't sense Shu with his Divine Sense. Only Sha could do it using her "feel". But it wasn't like Aldrich was clueless about what was happening behind all this.
Before going into the El Cid's Dungeon, it was indeed as said by the Crawler, Viscount Basajaun, that Aldrich didn't know how to use Perception. When the female Crawler appeared out of nowhere behind him from within the earth, he couldn't tell what was going on. At that time, he could only put it at the back of his mind to contemplate later.
It wasn't until he saw the Devil Aldrich sucking all his Divine Sense within him in Sha's memories that he formed a theory behind the secrets of Perception. And when he saw the memory of Devil Aldrich using that devastating Almighty Push, he got to confirm that theory. Even then, Aldrich's thoughts were fast enough to outrun the transfer of memories from Sha.
