IMO, shipping or 'dragging' a bike box through the airport is six of one, half dozen of the other. Ship it, and you'd be anxious if the bike will be there, be there on time, or make it in one piece. Carry it with you, and it can be highly awkward, ingress/egress trains/subways, etc. For me, the comfort of knowing it's with me, and fingers crossed it made the flight with me, is worth the inconvenience.
I've taken my bike with me everywhere - even to Rarotonga - with a Thule Roundtrip Transition hard case. It's not cheap, but well worth it if you plan to do more bike trips. I highly recommend it as Thule has been thoughtful in securing the bike in the box - check out YouTube videos. IMHO, I'd forget soft cases.