I don’t really know so this is basically an ass-pull, but “boner” as referring to an embarrassing public mistake seems to predate its use as referring to an erection, at least based on its relative frequency in innocent contexts. I assume this came to refer to an embarrassing public erection. You don’t really tend to hear it used in a flattering way. When it happens in a romance novel, it’s an “erection” or “engorged manhood”, when it happens right before a high schooler gets called up to the board, it’s a “boner”.