I'm very confused, what problem is wildcard routing causing? They talk about having to do an extra DB call but I don't see how that is the problem of the wildcard routing?

In the example (and from what I've seen in practice) wildcard routing is often used to make urls more human-readable. Something like mydomain.tld/post/123/here-is-the-post-title-but-its-not-used-for-lookup where only the "123" matters.