It isn't plausible that the baseband is routinely incorporating backdoors. However it is very plausible that nation states do lots of testing of baseband firmware, with an eye towards exploiting it. If baseband protocols were as easy to test as wifi we would probably see more vuln reports about them.
It is unlikely that they would be able to remotely update the baseband firmware though, especially on an iPhone. Also, an increasing number of baseband systems use highly verified kernels, such as sel4.
As to phones in flight mode routinely pinging, this is incorrect. It would easily be detected by standard tools and counter-surveillance equipment.
It isn't plausible that a modern phone would interfere with a modern jet IMO, but I still turn it to flight mode. Doesn't mean a passenger couldn't cause problems if they wanted too though -- turn on a GPS jammer and ADS-B/mode-S spoofer while onboard and watch everything go kooky.
A more realistic security problem is that of phones listening to wifi when turned off for geolocation purposes. Just the listening is exposing the stack to some degree.