Good question! Nobody was writing 1900 + (year % 100), right?
Some systems, where storing numbers in columns of characters were common practice (COBOL idiomatic style?) stored the date as two digits (possibly BCD), so the possible range is 00-99 no matter how many bits are used.
But it's worse than that. In the 90s a lot of code used 16-bit values, character strings. That is, it stored a char(2), parsed it as 2-digit number and then converted it to a date by adding 1900.
So it was only really "saving space" when compared with storing a char(4).
No punch cards or BCD, I'm talking about DOS/Windows systems.