Nobody is going to require you to insure
Management companies demand renters cover and verify it. An individual owner frequently does not raise it at all, which means the decision is entirely yours and the exposure is identical. Most uninsured tenants are uninsured because nobody asked rather than because they declined.
A claim between you and them gets personal
If you cause damage, a company pursues it through its insurer and nobody takes it personally. With a neighbor, the same claim is a conversation in the street. Your liability cover keeps that between insurers, which is worth more in a small community than anywhere else.
Repairs may be informal and should still be recorded
A small owner often fixes things quickly and without paperwork, which is a genuine advantage. Keeping your own written record of what you reported and when costs nothing and protects both of you if anything is ever disputed.