I would argue that if you start out knowing that you will switch, you essentially do lie, because you initially pretend to pick a box (or door) that you know you will not end up opening.
It is true that this approach adds additional layers of thinking, but the problem is that without those layers, the solution to the problem is simply not intuitive for the vast majority of people. Adding these additional layers helps at least some people gain a more intuitive understanding of why switching helps.
A much easier framing on a similar level is simply saying you pick a door, and then the host says you can either open the chosen door, or both other doors one at a time.
It’s the same thing. But if you don’t get why the state is unchanged even after opening one of the doors I don’t think you get it with this whole lying thing
It is true that this approach adds additional layers of thinking, but the problem is that without those layers, the solution to the problem is simply not intuitive for the vast majority of people. Adding these additional layers helps at least some people gain a more intuitive understanding of why switching helps.