The name of the currency usually precedes the value which is why "$" appears before the amount of dollars. This is the case for most currencies in the world.
The cents portion, however, comes about in a very different way. Where with units of the currency, one is saying something that is fairly sensible coming before or after the amount when speaking (though we like it better here in the US spoken after), with cents it only makes sense (sorry) coming after.
That's because you are saying "52 of 100" when you say 52 cents. That just cannot feel sensible warped about to come before the number of hundredths. Technically, I suppose it is no less sensible than putting the dollar sign first, but the dollar sign and the amount have no relation to each other: they aren't part of a phrase. The nature of cents makes the amount part of a complete phrase of amount and the hundredths idea. Even when it's centismos instead. So the cents comes afterwards always as it replaces that part of the phrase.
Given how long the "cents" part has been used without anyone thinking of its meaning as "hundredths of a dollar" one might say it's time to ditch the past and begin putting the sign first for consistency. But that wouldn't be consistent: the cents sign is not a currency symbol like the dollar sign, it is a subsidiary symbol meaning a particular way of dividing the actual currency. It's not about value, but rather about what the symbols actually mean: they mean very different things and so are treated differently.