In his new infrastructure push, President Donald Trump will embrace a longstanding goal of some aviation experts and lawmakers: transferring control of the nation’s air-traffic system to a new nonprofit corporation, which they say would mean a more nimble and cost-effective approach.

Control by the Federal Aviation Administration, these advocates say, is an antiquated model that falls short of the best practices used in other countries and has squelched upgrades that would allow planes to travel more efficiently.

Rep....