The bottom line here is that whether it's a good idea or not and whether WN ought to accept alternative docs such as a passport, doesn't help OP. Have to plan for providing a birth certificate or buying a seat.
It appears that OP is traveling in the US and lives outside the country. If that is the case, the possibility of cancelling and retaining the value for other tickets later and then looking for a bargain which might exist now on other carriers isn't an option (as it's also intimated that these are restricted).