In your first comment you said metric year, month, day. So it was unclear since a year and day are inherently solar concepts. It would have been clear if you just went straight to kiloseconds or similar.
You also did not include the Sun in your list which is a fairly big oversight if you meant to do away with the current solar day and year given the Sun is the dominant temporal determinant of our existing calendar system. You excluded the thing that gives the calendar its name. Getting rid of the (Sun and Moon) or (Sun, Earth, and Moon) would have been clearer than the ambiguous (Earth and Moon).
Exactly: earth+moon but no sun mentioned + ymd => year and day are solar things, month is a division of year and a multiple of day that already has little to do with cosmic things as a unit except that when grouped it lines up with seasons which is also a sun thing - equinoxes and solstices.
If we remove everything cosmic then we might as well do away entirely with ymd terms. kilosec, megasec, or whatever.
But! Removing the sun makes it immediately extremely impractical for scheduling: to schedule anything you'd have to constantly refer to an almanac - however rough - of the sun's position as, being completely removed from the sun and the biological constraints of circadian rhythm, time tracking will inevitably drift and offset to the point that it's impossible to reliably ensure actual people will be available for an appointment in 10ksec or 20Msec - whatever these secs are - in any intuitive or sensible manner that maps to the way biological beings fundamentally function, both at the solar day level (very fundamentally so) and the solar year level (less perceptible than day-level but still fundamental).
I mean, if I ask you what were you doing at 1610403576 unixsec or are you available at 1810403572 unixsec it is impossible to answer if you're even going to be sleeping well into the night without looking a sec-sun table (an almanac) up. The fact that unixsec as a duration is our current sec is immaterial - it could be anything so it might just as well be that one - as we just decided we're entirely removing the sun from the equation and defining secs in terms of fractional days would run against that. "well, I'll be sleeping" is the most common "not available" situation that we all share for ~1/3 of a day, everyday. Not exactly a corner case.
Consider that shops would not even be able to have "opening hours / days" signs on their door! Or dropping kids at school, setting an alarm clock, planning a trip to arrive at dinner... There's so much implicit scheduling around us that we're fixated on the comparatively small times where we have to open a calendar app (and even smaller when we have to cross timezones but that's not the topic of this specific thread). "I'm using a calendar already so everything might just as well be in the calendar" just doesn't stand up to the real world.
Since it's so impractical it follows that the only reasonable base unit of measure is not an arbitrary second† but the sun-bound day. The same argument can be run down for the four-beat-seasoned solar year, which allows us to intuitively grasp and anticipate so many things and organise as a civilisation - even when technology fails on us - that we take them for granted. And then, from that, we end up with a calendar shaped one way or another like the French Republican one.
† Even that could be challenged as our hearts beat at a rough ~1 beat/s at rest so there's a deeply grokked biological sense of time for us tied to that duration: 20s kind of resonates and that duration can be felt. Make the second half or twice and it's lost.
