> why an active mortgage

The banks make very low profits on 0% interest (government subsidised green) loans with a max total lending limit of NZD50k and many approvals might be less than $10k. The loan needs to use the home as collateral.

It wouldn't be cost effective (for bank or lender) to originate a new loan: instead the green loan uses the paperwork from an existing loan.

The bank can use the existing mortgage's legal paperwork to attach the new debt to the lender's house for collateral.

Approval, legal, and eligibility costs are reduced because an active loan has already been approved. The bank mostly wants to check that the lender's likelihood of repayment hasn't drastically worsened (e.g. lost their job).