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how often does anyone really transcribe a private key or an address by hand? I suspect extremely seldom. Almost to the point of never. We just do a copy with the keyboard and mouse, in which case, the font has no significance what-so-ever.
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Even when we "copy with the keyboard and mouse", it is important to be able to look at the original address and the copied address and make sure they are identical. Malware exists that can modify the contents of your clipboard. So, it's possible that you could copy an address, then the malware modifies the contents of the clipboard to be someone else's address, and then you paste that other person's address into wherever you are using it.
Generally you are correct though, we could use binary or octal, or hex, or any other base to represent the number. base 58 is what was chosen. It is both shorter than hex AND avoids ambiguity. Since it isn't really any more difficult for a computer to convert binary data to base58 than it is to convert that binary data to hex, why not?