These success of these avian flus are a direct result of mega factory farms ("concentrated animal feeding operations", or CAFOs) [0]. These massive operations are actually a relatively new thing since the 1990's [1].
We need to stop concentrating large numbers of animals at single sites.
The only way to change these practices is to make it more profitable by doing as you suggest (which I agree needs to be done). What are the carrots and sticks that could be used in such a situation?
You don't "carrot and stick" the construction industry to make buildings that are safe and accessible, the airplane industry to build and maintain safe planes, the auto industry to have have safe cars, and so on. Laws and regulations dictate certain levels of quality, and people follow them or go to prison. This has been incredibly effective and is the simple solution to this problem. It would be preferable for everyone to win, but it doesn't have to be more profitable - the dangerous behavior simply has to cease.
Bluntly, you don't carrot and stick criminals not to commit crimes. You make the behavior illegal and you punish criminals.
Carrots (in this case) would be subsidies and possible regulatory easements that might lesson relevant burdens if they are overly broad or excessively painful to follow (i.e., paperwork).
We need to stop concentrating large numbers of animals at single sites.
[0] https://www.liebertpub.com/doi/abs/10.1089/vbz.2006.6.338 [1] https://www.theguardian.com/environment/2023/jan/31/us-dairy...