That solution already exists actually. You buy a ticket/seat for the infant and use an FAA approved carrier. For example, the nuna pipa rx is FAA approved for this use.

It's not a popular choice because you have to pay full price for the seat, so lap-carrying the baby can save quite a bit of money. Once the baby is 2, you can no longer lap carry them, so that option goes away. There's FAA approved options for small children for whom the lap belt would be inappropriate that are different from the infant seats.