The problem is that especially nowadays where there are just not as many mice and people have cats for emotional reasons rather than us working animals, cats are responsible for killing off local songbird populations and otherwise damaging if not collapsing ecosystems because they are effectively invasive species in most places of the world. Famously, Australia is probably the best example, where cats are/have devastated the ecosystems, including pushing around 30 species near extinction, along with all the other problems due to invasive species.

Unless you have a barn where mice thrive, it is not advisable to let them out to eradicate the local songbird or amphibian populations.