Here's my two cents

. The princess is indeed a descendant of Alice. The reason why Elysium collapsed is because Alice & co. were taking their sweet revenge against them and established a new ruling monarch family. But alas, humans are human. The new guild is now corrupted once again.
Or
They were taking advantage of the chaos of war to establish a new country or some shit.
Edit: Never mind, it's probably coincidence that she inherited Alice's lineage. The MC seems like not an idiot. If the kingdom is a new one, he should notice something when reading books in the library.
