Proper border checks don't do much if people enter the country legally but overstay their visas

IDs (along with verification laws) discourage employers from hiring unauthorized immigrants, and without access to gainful employment, many will opt to return to their country of origin, or choose not to come in the first place.

My understanding is that it makes checking job eligibility easier, so enforcement of non compliance is easier.

A big source of illegal immigration is visa overstay (https://migrationobservatory.ox.ac.uk/resources/briefings/un...), which ID can solve by tracking the visa status.

There are benefits to UK citizens, such as being easier to open a bank account and to comply with Voter ID laws.