Should the person who has ownership rights in an insurance policy and the insured be relatives?

The question does not really involve "should". The direct answer is "no".

Using life insurance as an example, the owner of the policy is often the person who pays the premium. The insurance contract gives the owner various rights, such as to initially designate the beneficiary, change the beneficiary, pledge the policy as security for a loan, and other acts.

The insured is the person whose life is, well, insured. Stated otherwise, this means that when the insured dies, the insurance company generally pays the death benefit to the beneficiary.