Criminal background check is a common requirement in many employment types and for many organizations (specially the regulated ones) it can be a regulatory or legal requirement to perform a criminal background check before they are hire individuals on certain positions.
These positions mostly include the employment types that include healthcare, financial, insurance or services that encompass vulnerable population (such as old age people, children, disabled, etc.).
Since there is a scope of taking undue advantage of resources or people by an individual with criminal background, criminal background check is a precautionary measure against it. E-verify, however, is not the process to perform criminal background checks.