I mostly agree, but I would say, there is an advantage to having the extra guy but it's pretty marginal.
If Lanning 'pretended to make a defensive switch' right as Ohio State was about to snap the ball, and he left 22 defenders on the field, then that would actually make more sense as a way to exploit the rule. Tough to complete a pass with 22 defenders. Wastes a few seconds off the clock; Ohio State gains a mere 5 yards off the penalty, but they lose 4 seconds off the clock (which is more valuable in the situation). In fact, they might lose more than 4 seconds, because the QB might be so confused about what to do, he just panics.
But just 1 extra guy only marginally improves the odds of getting a defensive stop and would bail out Ohio State if they screwed up (e.g. completes a pass in-bounds but not for a 1st down - the 12 men penalty then stops the clock that would've run out).
To me, it feels like this was unintentional, but worked out brilliantly for Lanning, and he'd rather spin it as a 'brilliant move' than a Derek Dooley 'oopsie I have 13 guys on the field' moment.