Delegating the work does not delegate the risk
A property manager collects rent, arranges repairs and deals with tenants. The owner remains the owner, and a claim arising from the condition of the property is normally made against the owner regardless of who was supposed to be looking after it. Your policy is what answers, and the manager’s own insurance protects them rather than you.
Both directions need naming
Management agreements commonly require the owner to name the manager as an additional insured, and sensible owners ask for a certificate from the manager in return. Each side is protecting itself, and an owner who signs the first half without asking for the second has made a one-sided arrangement.
Nobody is checking the property but them
Small problems that an owner living nearby would notice can run for months under remote management: a slow leak, a failing roof, a tenant doing something the lease forbids. Gradual damage is excluded on these forms, so the loss that follows is frequently uninsured.