For Waite, at least in the PKT, the question of full face or profile wasn’t an issue. From the PKT, Class 1, Section 2:
The Empress, who is sometimes represented with full face, while her correspondence, the Emperor, is in profile. As there has been some tendency to ascribe a symbolical significance to this distinction, it seems desirable to say that it carries no inner meaning.
As to the throne, I found something in Book-T that might help explain it:
The Four Queens are seated upon Thrones, representing the Forces of the He of the Name [YHVH] in each suit; the Mother and bringer-forth of Material Forces: a force which develops and realizes that of the King: a force steady and unshaken, but not rapid, though enduring. It is therefore symbolized by a Figure seated upon a Throne: but also clothed in Armour.
The Queens sit on thrones
because of everything said before—Material Forces, steady and unshaken, not rapid, enduring. This part deals with the Queens and not the major arcana, but it reflects thinking that could transfer to the majors as well.
In the GD tarot, the cards in which the figures are seated on thrones are—Empress, Emperor, Hierophant, Justice. In the Waite-Smith they’re the same with the exception of the Empress. Waite’s descriptions for each of these cards contain language that puts them either on an external or mundane level.
Empress = Earthly, inferior, this world.
Emperor = this world, mundane.
Hierophant = external, exoteric, outer side of life, manifest side, world of institution.
Justice = the pillars of Justice open into one world and the pillars of the High Priestess into another.
The thrones could be clues that indicate the symbolism represents something mundane or of this world. Granted, it’s all circumstantial, but it could be one explanation.
For Waite, the symbolism of the cubic stone had another significance pertaining to the "white stone" of Revelation 2:17. I think that might be what he meant by "confuses some of the issues."