Does it make sense for a couple to apply for credit under one name?

There are certainly cases where this is the case. Let's say that after you get married, one spouse has much better credit than the other one. If you apply jointly, the interest rate would most likely be higher due to the second spouse's worse credit score.

As long as the first spouse brings in enough income to qualify all by himself/herself, this can mean a significant amount of savings over time.

Just remember, the person who has his/her name on the account will be the one solely responsible for its payment.