Directly exposing Gray the Lich's identity would indeed bring substantial benefits, but it obviously does not align with the principle of maximizing the interests of the Dragon Clan.
However, negotiating with a fanatic is a major issue. After all, true faith, from the beginning, is never something that can be negotiated. Since Gray appeared on the continent, the only person who successfully negotiated and reached an agreement with him was Pope Augustus III. That was only because Augustus III had a similar view to Gray on certain matters. Without this, no matter how capable Augustus III was, he wouldn't have been able to make Gray submit.
This is because there is a vow in the Knight's oath – sacrifice, sacrifice for comrades, sacrifice for faith. When your opponent takes pride in sacrifice, there seems to be no room for compromise.
This left the Dragon Clan, known for being petty, calculative, and profit-driven, extremely troubled.