Except it would be absolutely impractical to actually use in practice by any species/societies that have to sleep on a regular basis and in general need cycles. If all your "natural cycles" happen to fit well into base-10, well, that's great. Otherwise, you need to base your cycles on something else, which is exactly what calendars do.
And, just by the way, the Gregorian calendar is bad and messy, but the ideas it's built upon are absolutely great and are not results of shower-thinking and twitter-shitposting, but arise from pure practicality. They suit Earth, and humans are earthlings, their cycles are defined by the Earth. A year is a crucial cycle, because it defines weather so much. A day is a crucial cycle, because it defines when it's dark outside. A lunar month is a natural and pretty good cycle, because Moon cycles do actually affect life on Earth, but it isn't crucial, which is exactly the reason, why Gregorian calendar happens to get away with pretty much ignoring this one, unlike a day and a year. Still, it explains why most calendars through history prefer months being close to 27.3 days, and why weeks are 7 days (a quarter of 28). Both cycles also are both long enough and short enough to be useful for practical reasons, like organizing work schedules even without relying on celestial bodies. Furthermore, it even appears they are not enough, which is why the year is divided into "quarters" for business purposes like accounting. And these happen to be fairly close to 30 days, which happens to be a very neat divider of 360, which is close enough to a year on the one side, and a very neat number that naturally divides all small numbers up to 6 on the other side, which makes it easy to work with (unlike base-10, BTW, since that cannot be divided by 3).
All of which explains, why French Republican calendar is actually a great idea and unfortunately failed (for a fairly stupid reason, IMO), and base-10 day is not so great (although it has merit, since modern digits are base-10) and naturally failed.
Now, these totally imaginary and having nothing to do with reality aliens of yours may not have earth-like and human-like cycles, but they surely have cycles of their own. So it is unlikely that magnitude-1000 time measurement with no cycles in-between can work for them either.