Switching the Knight and the Bishop

When I analyzed one of those mistaken beginner setups in which the knight and bishop are switched using a chess engine, here's what I found:
1) It actually seems as if the position is more equal with the swap than without, though the difference is quite tiny.
2) Some of the best openings came as a surprise. In the normal setup, the computer determines that the very commonly used Queen's pawn, King's pawn, and Réti openings are the most optimal. When the bishop and knight are switched, 1.d4 remains as the computer's favorite choice. However, the chess engine also suggested 1.c3, 1.e4, and 1.f3. The 1.e4 is understood, but why the 1.c3 or 1.f3? And why is it that in some cases they even surpass the superiority of 1.e4 in the computer evaluation? I feel that the engine probably found them good due to the following reasons: most importantly, it allows for the control of the bishop diagonals; it also does not block the knights' moves like these do in the normal setup; and they are very supportive of the center pawns. Besides all of the above, the computer also likes Nb3 as well as h4, Nd3, c4, etc., though the last three seem to give black a slight advantage. By the way, I decided not to analyze after the first move for some reason, so feel free to experiment with various opening variations. However, you could also just search things up perhaps, because I doubt that this setup has not been explored before, though I myself stumbled upon it without doing any research.

Also, a final note: does this setup have a name? Since like I expressed before, I strongly feel that various people have investigated it before me. So does it have some kind of title?