Yes, we've already established that your level of acceptable risk is extremely low - the amounts found there are Less than in the study I previously linked.All birds have lice. All the time. There is no such thing as a bird, wild or domestic, that does not have lice unless they've been recently treated for lice. I never said the rest of our birds had no lice.
Furthermore, Permethrin is not only toxic to cats (check the label on the bottle if you don't believe that) but it is also toxic to beneficial insects such as honeybees, butterflies, moths, and so forth. I will never ever spray or dust the entire premises with Permethrin.
Next time you use it, think about what you are doing.
Really, I've got plenty to do besides quibble about teeny statistics.
Here's the study:
https://pubmed.ncbi.nlm.nih.gov/7343077/
Based on that study, I personally would not eat eggs or the meat of treated chickens for at least 3 weeks after treatment. I don't care that the bottle does not specify withdrawal period. Think what you like, but Insecticides are dangerous.
If you lived your life by similar levels of acceptable risk in other common endeavors, you would be paralyzed by fear.
You've given up wheat? grains generally? nuts, fruit, beef, cow's milk, cheese, a host of green leafy vegetables? and you feed your birds a diet absent in such things as well?
You may choose not to use permethrin on your birds, but lets not pretend that has anything to do with a science based approach to the use of permethrin generally - as the trace amounts found in egg yolks after treatment are far lower than the levels acceptable in a host of other foods neither yourself, nor your birds, likely avoid.
Ignorance may be bliss, it may even be reasonable, but you are swatting at flies while elephants stomp about the room.