When does it not really work?...
As I've pointed out here on many occasions, and which no one has yet given a sensible answer to - if this was such a desirable and valuable alternative tactic, then why do none of the most successful sides in the world in recent years (Arsenal, City, Liverpool, PSG, Bayern etc.) regularly use as a plan B a left-sided winger on the left (or right-sided on the right)? It's basically never bothered with, and none of the top wingers in the world are players who play on the same side as their favoured foot.
The only players who could do that fully in the manner you describe and apparently desire are those who are so two-footed it basically makes no difference to them. The only player like that really on the market is Diomande.
It is interesting though you turn your nose up at Rogers for this as well (though he is very right footed). Rogers has actually played a not insignificant 18 times for Villa on the right flank, where he is more of a passer/crosser of the ball (as opposed to his cut-inside and finish merchanting from the left), and has racked 9 assists and 1 goal in that time (an assist or goal every 149 minutes). Not too shabby...