In principle I agree with your reasoning, almost but not quite. In my humble opinion I could also say:
"Tomorrow I have to depart (I will take a plane) for London to take part in a gala dinner under the aegis of the Queen of England."
If you don’t mind I could traverse the distance to London by sea with the help of my old reliable yacht but that will take too more time and it is most likely that I’ll be late. In this instance I hope, I could even use the verb “sail” = “depart”.
With the help of the following examples I will try to persuade you that “depart” = “leave”. (Not only in relation to travel.)
…let me depart your presence. (do you think I have to hire a plane or train ? )
Trust members with an exclusive invitation to stay at the hotel and depart with a case of specially selected wine from The Lygon Arms' cellar.
The Home Office is not bound by those opinions, and appears to depart from them frequently.
Hitler exhorted the Party and nation to maintain discipline, and not to depart from the path of legality in the matter.
….but there is a willingness to depart from it in certain circumstances.
In so doing I depart somewhat from studies of working-class involvement in the formal political sphere during the twentieth century..
It now seems clearly established that the Court of Appeal may only depart from one of its own previous decisions in four circumstances.
Nor do I feel compelled to depart from that conclusion by the fact that, under the present practice,
The local authority may depart from the terms of any order under section 34 …
Whether Secretary of State entitled to depart from judicial recommendation
They depart from the perspective of the constitutional authorities, however, in their advocacy of proposals..
But Moscow remains unwilling to depart from the Vietnamese conception of a settlement.
Remember, you must arrive at and depart from your chosen hotel on the correct day.
Winter visitors depart in late February and March, when our breeding birds also return inland,
… and thousands of birds arrive and depart unseen.