Wasn't it Irving Berlin, or one of the old time songwriters that could only play in a few keys? He had a special Steinway made that moved the entire action sideways, so that it could sound in different keys! Early high-tech transpositional technology...!
Si, I guess the question should be, does it matter, as long as you transpose to different keys? Sonically, it is identical to playing in the perceived key.....
My answer would be... No, not really, but....... most songs involve some transposition within the song. The bridge may go to another, often related (sometimes not!) key, there may be changes from major to minor (sounds like a good lyric there!), and unless you can play fluently in any key, there may be whole sections of many, many songs that you will not be able to play, no matter if you START in 'C'...!
So break out that Hanon, or figure out a nice jazzy cycle of fifths exercise, and start to come to grips with other keys than 'C', or you may HAVE to play country for the rest of your life!
(Just kidding, all you country fans!

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