For starters buying two single life policies can be cheaper (or at least no more expensive) than say buying one joint life second death policy (i.e. a policy that pays out when the second person dies). This type of policy is typically used to cover an outstanding inheritance tax bill.
This is particularly the case if either life being assured has a medical condition whose level of risk to the insurer may be assessed more favourably by one insurer than another, resulting in a cheaper premium. Or to put it another way, if you take out separate life insurance policies then you each will be underwritten separately on your own merits or otherwise. Consequently you could take out life insurance policies with different insurers, namely the ones offering you each the best and most cost effective cover.
Generally taking out two separate life policies will at worst be marginally more expensive but you will get twice the pay out if you both die during the insured period of time. With a joint life policy there would only be a single payout.
Also if you took out a joint life first death policy (often used when covering an outstanding mortgage), the policy would pay out and then cease in the event of either of you dying during the policy term. This would leave the surviving spouse having to take out a new life policy, if required, which may be more expensive as they are that bit older.
Finally as each life insured would have separate life policies they could easily be distributed separately under the terms of separate wills or trusts.
So don’t just assume a joint life policy is best for you. If you are unsure then seek professional advice.