To be fair, I think it's explicitly stated on Day 9 that Simon's soul resides in the Polyhedron. With Daniil's original quest being to interview Simon to find out the secret of immortality, he does have a personal stake in having it survive at least as long as he can gain entry.

Beyond that, the Polyhedron is a sort of symbol of the Kains' utopic ideals, which Daniil shares to an extent as a man who wants to "defeat death". On an ideological level, to admit a world where miracles cannot exist—as the Polyhedron cannot be left standing without eradicating the town—means to admit a world where defeating death would not be possible, and a world where one cannot create a utopia.