Why is the unit of measure placed before the value for currencies? (2016)

It isn't always. For smaller amounts you can just as well see something like 5¢. But you will never see a price listed using both formats, like "$1 5¢" or whatever.

Quebec, in Canada, puts dollars, pounds, euros, at the end of the number. And Brazil uses it as a divider between units, like the way electronics might use 1R5 to designate a 1.5 ohm resistor. It looks like 19$95, but with the old double-striped dollar symbol, and meaning Reals instead. Bonus: The double-striped $ is called a cifrão, and has nothing to do with the initials US.

Also, I see the Euro sign after a space at the end of a number all the time. For example, 199 €.

I think the question is essentially wrong. The unit of measure is only placed before some currencies, and in some languages.