They're doing something wrong. And they have to fix it. They could start with fixing their customer experience.They're definitely doing something wrong, and they definitely need to fix it.
I like your redesign, but I doubt that their existing design is what's losing them 1.2 billion a year.
Treat this as a pandemic emergency across your entire company /
Immediately fire your entire web team, if you have one /
[Booking a flight on your website] disturbed me so deeply that I vowed never to fly your airline again
This comes across as hysterical and out of proportion with the problem at hand. This detracts from your main points, and makes it more difficult for you to be taken seriously.