Earlier quoted context omitted.
My understanding is that the actual number of bits used would generally have been 4 bits per digit, as they were using Binary Coded Decimal [1]. So dropping the 19 would save you a byte per date. Sure, they could have used a custom encoding. But that increases maintenance cost and extra development work. All to solve a problem that nobody cared about at the time. [1] https://en.wikipedia.org/wiki/Binary-coded_decimal
Just seems wierd. A 2 byte day count would give a huge range and use 2 bytes for the full date Vs 3 bytes for a BCD yymmdd representation.
It means that data interchange is now much more complicated too. How do you get everybody to agree on the same 2-byte representation for dates? This is the 1960s, so you can't just email them. You have to have somebody type up a letter and mail it. Or if you want to get on the phone, a 3-minute international call will cost $12, which is about $100 in 2017 dollars.
Plus then you can't look at a hex dump or a punch card or front panel lights and see the date, so now you've made debugging much harder.