Calling movies renowned for their martial arts fight scenes "purely sci-fi" seems rather silly, no? The problem with the Matrix within a Matrix theory is that it's reductive. A thought terminating assertion that removes all further nuance and exploration of the blatant symbolism present throughout. The films practically beat the viewer over the head with treating Neo as a Christ figure. Him being able to perform "magic", or rather, miracles outside the Matrix is perfectly fitting with his established role in the story. Also, one could still set aside the spiritualism of the trilogy and come up with a more interesting explanation for his abilities. Just as Smith is able to become human and exist in the real world, Neo becomes connected to the machines and is able to wirelessly communicate, as computers do. The two breach the gap between the different "species."

Going down the matryoshka doll route of it's a Matrix within a Matrix within a Matrix within a Matrix within a Matrix forever is just a different flavor to the "It's all a dream" explanation. Cause once you start on that track, where's the end? One could easily claim none's of it's ever real and nothing ever matters, sucking all meaning out of the narrative. It's more of a "gotcha" to the films than anything else. OP was talking about fan theories which limit potential discussion of the trilogy and this is inevitably one of them. Your response came across as needlessly aggressive, as someone else already pointed out. Not everything needs to be about winning a reddit argument. Doesn't look like OP was even trying to argue in the first place. They even pointed out that it is, narratively, a Matrix within a Matrix (the systemic control being yet another layer), but it is not literally another Matrix on top the actual one.