No, I think it's all part of the magic of comics. The simple fact that a building full of newspaper reporters never seems tro twig that when Clark is about, SM isn't, and vice versa, and that's before we get to the glarlingly obvious physical similarities.
Actually, Mike Yarwood used to employ a similar technique - after an hour of dubious 'impressions;, he would sing (very badly!) a song and preface it with "...and this is me ...." and the scales would fall from the viewers' eyes and we would realise that the characters that had lost us the will to live in the preceeding eons of time were all in fact ... him!
How amazed we were - so much so, that we forgot it all it until he did it again the next week.
Only problem is, Superman is a comic-strip character, whereas Mr Yarwood was more of a tragedy masquerading as light ... a-ho-ho-hee-hee-hah-hah ... 'entertainment'.