What Athenians valued in Theseus was not the Minotaur. It was the synoikismos, the act by which he is said to have dissolved the separate councils and magistracies of the villages of Attica and gathered them into one city with a single government, then invited outsiders in and, in some accounts, resigned much of his own power to the people.
That is a founder narrative built to justify a specific constitution, and Athens curated it accordingly. In the fifth century BCE, on an oracle's instruction, the Athenians located bones on the island of Skyros which they identified as his, brought them home, and built a shrine in the city to house them. He acquired a festival, the Theseia; he appears on the sculpture of public buildings fighting centaurs and Amazons, in scenes that stood for civilisation defeating disorder; and Athenian writers steadily improved him.
The result is a hero doing political work. When a state wants to say that its arrangements are ancient rather than recent, it needs someone to have made them, and Theseus was available. The atlas records both layers: an old Attic hero with the usual monster-killing repertoire, and the deliberate later construction of a democratic founder on top of him, which is the more interesting of the two because the construction can be watched happening.