Yes. Sport horses and show horses are transported by air on a regular basis.
I'm sure they have some acclimatization experience and travel with a trainer or other equine experts. I'm sure they travel in special containers. I'm sure there might be two together, but not four together with no partitions.
There might be some ways it could be improved, but one of the big problems is the length of the journey. Lots of the horses flying from the United States to Europe, or flying around in the United States, have journeys of only five or six hours, which is reasonable, especially if they're in those accommodations that are appropriate for a horse, and with proper supervision.
With what's happening at the moment—flying from Canada to Japan with these four horses in the same partition for this hugely long period of time, with no water and no food—and you addressed each one of these issues one by one, it would probably be uneconomical financially and not a deal for the $20-million-a-year industry.
However, that would be the way that it could be made acceptable.