Domestic sacrifice

The arch of Constantine in Rome depicts a bear and boar hunt that ends with a sacrifice to Hercules. Architectural historians suggest that the hunt represents Constantine’s taming of the forces of civil disorder and chaos. One (Mark Wilson Jones) suggests that the sacrifice represents pre-Constantinian pagan religion, while Constantine’s participation in the hunt represents his conquest of bestial social and religious forces.

My interest is elsewhere: Biblical sacrifices were confined to clean animals, and, more specifically, to domesticated clean animals. No wild animal ever ascended to Yahweh’s altar?

What does it say about Israel that it offered only domesticated animals? What does it say that Israel detached the cult from the hunt?