Cents were a useful unit back when a dollar was defined as 1/20th of an ounce of gold (or 1/35 between the Great Depression and 1970).
In the UK, we also used to type '£' with an 'L' and backspacing and overtyping an '='.
Weirdly, I learned to type on a second hand Selectric typewriter that my parents bought cheaply at some auction, and while it had a '1' key, the only ball we had used that key for punctuation instead, so we still needed to type 'l' instead.
And since I've mentioned GNU groff elsethread, here's where it today in its "ascii" mode uses a minus sign instead of the equals sign to do the very same thing as you did on your typewriter, for "Po", the macro for producing a pound symbol.
* https://cgit.git.savannah.gnu.org/cgit/groff.git/tree/tmac/t...
The typewriter I grew up with simply didn't have a key for it. It also didn't have a 0 or an exclamation mark or a plus sign. There were well known substitutes:
For the number 1, type lowercase letter l.
For the number 0, type uppercase letter o.
For the exclamation mark, type a period, hit backspace, and type an apostrophe / single quote.
For the plus sign, I'm not aware of a good substitute. You could maybe superimpose a slash on a hyphen, but it would look bad.
There was no division sign, and using a slash to denote division was not yet something I'd ever seen anyone do. You could probably have superimposed a hyphen and a colon to get ÷.
Oddly enough, it did have other characters which you won't find on a standard US keyboard today: ¼, ½, and ¢. The cent sign was useful, and it seems logical to me that if you're going to have $ you should have ¢ too!