Childbirth can be quite loud, distressing to others in the house, and very messy. There were no laundromats. Being on nice clean straw might have been preferable all the way around.
I'm going with the "space at a premium during the census" theory above.
You’ll recall the perpetual fame promised by Jesus for the woman who poured the expensive perfume over him. Someone, I suspect, forfeited similar notoriety by missing this opportunity for the ultimate in hospitality.