The longer Auron and Alice took down the cult, the more victim would be. Not only that, but Auron also pretended to be sick because of the not yet perfect device. If every time he joined the meeting, he was ill, then it would arouse suspicion from the other.
Moreover, from the previous meeting, Auron could see that the leader of the meeting was cautious in managing everything.
After tying the hostages, Auron faced Alice, who was still thinking. She actually had a plan. If the plan was a success, they could infiltrate the cult secretly. However, the risk was too significant.
The difficulty of making the plan was placed on the secrecy of the plan. They would need to infiltrate inside the cult at least for one day without getting exposed.