I have an S&S coupled bike that I've flown with for 10 years. I pack it in the hard shell case. The case takes a real beating. From both the airline gorillas and the various TSA-types around the world.

While the box you describe will hold your disassembled bike, will it hold up when shoved into a tight space or on the bottom of a large pile of other luggage? Also, a disassembled bike has sharp edges that might poke through or distort the box under weight pressure or when being shoved back into the box by uncaring TSA goons. My hard shell case, which might not be all that more durable than your coroplast, has spots that have been distorted by the tip of the wheel (what the fork sits on where the axle goes) through compression over the years.

Things to consider when building the box:

How are you going to carry it? You will need a handle of some sort to lift it up/down stairs.

Will it have wheels? Otherwise, moving a packed bike down a long corridor or from the bus stop to a host's house is a major effort.

How hard it is to open and inspect? The TSA will likely open it every time you fly (they do mine). They are very hard on clasps, compression straps, and luggage. One of the two latches on my bike box no longer works as a result of some careless TSA reassembly. I've also had compression straps (now needed due to the latch problem) disappear.

How will you pad the bike parts? Packing a disassembled bike in a box results in lots of (painted) metal to metal contact. The parts need to be protected from one another and even then paint gets chipped off and parts bend.

While the hard shell cases are, indeed, expensive, consider how you would deal with arriving at your starting point with a broken coroplast box. My box is getting to the end of its useful life. I sort of hold my breath every time I wait for it to come down the baggage chute.

While building it is cheap comparatively, I suspect you won't get it right the first time(s), so will have to perfect it over a few iterations. In the end, it might save you money or it might not. The same can be said for it protecting your disassembled bike.