There's no specific grammatical rule saying the phrasal verb to take off can't be used transitively - it's just that native speakers don't normally use it that way. This example...
Mr. Waicott did not have that authority, that permission, from the duty officer to take off his plane.
...is from an Indian Parliament debate transcript, so it might be from a non-native speaker. But the surrounding text is impeccable English, and I personally wouldn't assume "non-native speaker!" just because he made the best of bad situation. That's to say we don't have a well-known alternative verb that can be used instead.
Here are a couple more written instances, more obviously from native speakers...
Given a long enough runway, it would be possible to take off our plane [loaded up to 10 tons].
[the way to do it is for you] ... to take off your plane, and land it at Washington National Airport.
In short, I suggest you copy native speakers - where possible, rephrase so you don't need a transitive verb; if you can't do that, just bulldoze through and use take off anyway. You'll always be understood.
There are probably other even less idiomatic terms than to make a plane airborne (perhaps relevant in specific technical contexts), but you'd probably not want to use them in more general contexts.