This topic has been around several times before. My DH & I both have hard cases and both fly with our bikes. Lots.
In the early days I shipped my bike & did not have any damage to the bike itself, but one time the box (cardboard) had a huge hole in it and the bottle cages & one skewer had fallen out somewhere along the line. That is when I decided to invest in a hard case. DH did the same.
We have never - NEVER - had problems flying with our bikes. We fly Frontier and as far as I am concerned, they are a stellar airline when it comes to handling our bikes. They still "only" charge $50 each way - much cheaper than trying to ship.
One advantage to traveling with the bikes is that you would have them available to ride right up until you pack to leave. Packing, once you get the hang of it, takes about 30 minutes tops.
Good luck, whatever you decide to do, and most of all have fun!
"When I'm on my bike I forget about things like age. I just have fun." Kathy Sessler
2006 Independent Fabrication Custom Ti Crown Jewel (Road, though she has been known to go just about anywhere)/Specialized Jett