He's probably keeping it from Koichi so that he's not, in a way coercing him to stay out of that obligation.
like if kouichi asked him he would tell him but you know at the same time it's one of those put yourself before someone else situations.
It really doesn't seem like it would occur to him to ask what cost Caius has to pay for the summoning magic to both bring Koichi over to Eustil and send him back to Earth or the incomplete familiar contract....given that it's pretty much expressly stated at the beginning of the story that the use of summoning magic in such a way on such
A large scale is forbidden and seems like the type of thing that a group of people should attempt not a single individual.
You know...Caius has always been telling Kouichi the truth but there is a part that he is leaving out so that Kouichi can leave if he wants to. Kouichi could literally be so happy with Caius but I can also understand why he wants to go back. I hope that Kouichi realizes that his mom just wanted his happiness and now you have Caius who just wants his happiness too.