Not to be facetious, but if a tuxedo didn't have satin lapels and satin stripes down the sides of the pants, it'd just be another black suit. I mean, the former is probably the single most common characteristic differentiating a tuxedo jacket from an ordinary black jacket, and the latter the single most common characteristic differentiating tuxedo pants from ordinary black pants.
Yes, there may well be other, less common or more subtle differences, but the satin thing is the almost universal and immediately obvious one. Also, there may be differences in accompanying items - cummerbund, shoes, shirt studs, etc. But they're just that - accompanying items, and not the tuxedo itself. And for purposes of this post, "satin" should be taken to technically mean "satin or grosgrain."
It's sort of similar to the reason why tricycles have a third wheel - it's because without that third wheel, they'd just be bicycles.
So it's essentially there for the sole purpose of distinguishing it from a suit?
Well that's rather anticlimactic; I though there would've been some 'practical' reason as to why those features existed.
Nevertheless, thanks for the explanation.