Jet engines don't go anywhere without a large industry continuously taking care of all the complexity that even the simplest jet travel imply.

They also kill a lot more people when they fail.

Birds don't need airports, don't need expensive maintenance every N hours of flight, they run on seeds and bugs found everywhere that they find themselves, instead of expensive poisonous fuel that must be fed to planes by mechanics, they self-replicate for cheap, and the noises they produce are pleasant rather than deafening.