What is the case law in the United States when it comes to the case of a lay-man who is not qualified to stand trial?

I do not rely on the thinking expressed by Black J. in Gideon v. Wainwright (1963), 372 U.S. 335, 9 L. ed. 2d 799, 83 S. Ct. 792, 93 A.L.R. 2d 733 at 805, who quoted the following passage from a judgment of Sutherland J. in Powell v. Alabama (1932), 287 U.S. 45 at 68, 77 L. ed. 158: “Left without the aid of counsel he [even the intelligent and educated layman] may be put on trial without a proper charge, and convicted upon incompetent evidence, or evidence irrelevant to the issue or otherwise inadmissible.”

As Seaton J.A. said in Regina v. Ewing at [W.W.R.] p. 239, that suggestion “has no application to a trial in this jurisdiction today”. By that I infer that Seaton J.A. was referring to the position accepted in Alberta as no doubt in British Columbia, but perhaps not in the United States, that the trial judge has a duty (even if there is defence counsel and he makes a mistake) “to see that only proper evidence was before the jury… [The judge] must take care that the prisoner is not convicted on any but legal evidence” (per Wills J. in Regina v. Gibson (1887), 18 Q.B.D. 537 at 543).