Depends on the "they"...

But generally, back in the day data storage, memory and processing power were expensive. Multiple factors more expensive than they are now. Storing a year with two digits instead of four was a saving worth making. Over time, some people just kept doing what they had been doing. Some people just learned from mentors to do it that way, and kept doing it.

It was somewhat expected that systems would improve and over time that saving wouldn't be needed. Which was true. By the year 2000 "modern" systems didn't need to make that saving. But there was a lot of old code and systems that were still running just fine, that hadn't been updated to modern code/hardware. it became a bit of a rush job at the end to make the same upgrade.

There is a similar issue coming up in the year 2038. A lot of computing platforms store dates as the number of seconds since the beginning of 1970-01-01 UTC. As I type this comment there have been 1,710,757,161 seconds since that date. It's a simple way to store time/date in a way that can be converted back to a human readable format quite easily. I've written a lot of code which does exactly this. I've also written lot of code and data storage systems that store this number as a 32bit integer. Without drilling down into what that means, the limit of that data storage type will be a count of 4,294,967,296. That means at 2038-01-19 03:14:07 UTC, some of my old code will break, because it wont be able to properly store the dates.

I no longer work for that employer, I no longer maintain that code. Back when I wrote that code, a 32bit integer made sense. If I wrote new code now, I would use a different data type that would last longer. If my old code is still in use then someone is going to have to update it. Because of the way business, software and humans work. I don't expect anyone will patch that code until sometime around the year 2037.

Yeah I would imagine poor/lazy planning or they either thought their tools would be replaced by then and/or that computers were just a fad so there's no way they'd be used in the year 2000.

you think that's bad, just wait til 2038 when the UNIX time rolls over.

The Mayans figured a calendar that only went to 2012 would be good enough. And they were right, their civilization didn't exist anymore in 2012. Only relevance their calendar system had in 2012 was that some people felt like it was a prophecy about the end of the world. Nope, just was an arbitrary date the Mayans rightly assumed would be far enough away it wouldn't matter.

While I suppose you could make a date format that was infinitely expandable, it would take more processing power and is really unnecessary.

Anyway got until 2038 until we'll have to deal with a popular date format running out of bits. We'll probably be in some kind of mad max post apocalyptic world before then so it won't matter.

Some of the software at my employer at the time, would have failed. In particular, I fixed some currency trading software

When you think about it storing a date with 6 bytes would take more space than using Unix time which would give both time and date in four bytes. Y2K38 is the real problem. Y2K was a problem with software written by poor devs that were trying to save disk space by actually using more disk space than needed.

This comes to mind:

You don’t store dates as Unix time. Unix timestamps indicate a specific point in time. Dates are not a specific point in time.