A joint "First to die" policy is an effective way for one partner to leave an inheritance to help support the survivor, but it is not a replacement for having a separate policy on each person. First, this type of insurance policy tends to be more difficult to find and more expensive to buy than other types of coverage, because the risk of an early pay out are doubled when there are two lives combined into one policy.
A "First to die" policy has a distinct disadvantage as a combined policy: It will only pay out once. The first person to die will trigger the maturity of the policy and the policy will settle. If the second person dies shortly afterward, the policy, which would already be closed, would not provide any benefits for family members. If leaving an inheritance is important, it might make more financial sense to get a "second to die" policy which will not pay out until both insured parties have passed away. In this case, there would not be any inheritance for the surviving partner, but when that person passed away there would be a settlement for the named beneficiary in the policy.
If both partners were covered by individual life insurance policies, then the first to die would trigger the first policy, potentially becoming a financial rescue for the surviving partner. And when that partner passes on, the second life insurance policy would trigger, paying out to whoever was named as the beneficiary. Your insurance agent can write the policies so that the policy of the first to die pays to the survivor and the policy of the second to die pays to another beneficiary, regardless of which partner passes away first.
A first to die policy is more useful in a situation where there are no survivors beyond the partners. When the first partner passes away, the survivor would receive the life insurance benefits, and there would not be a policy for the second partner. Even in this situation, though, it will usually be more economical to use a different life insurance strategy. You could do it this way, but it is not the most efficient use of your life insurance investment.