Let's make a day be 86400 seconds (already a SI standard), and then you can divide that into tenths, hundreds or whatever. One thousand of a day is 84.4 seconds, which is close to a minute (which is (/ 60 (/ 24 one-day))).
We have metric for measurements in space, but something as simple for day-to-day time measurement would be nice.
I'm sorry I'm making fun of you, but I just can't help myself as this happens all the time -- somebody comes up with a reasonable idea, and then the next commenter takes it so widely out of proportion, willing to re-engineer the whole society just to marginally improve his own comfort.
It's not a bad idea in principle, but the massive cost of switching wouldn't be worth the marginal gains.
Why not keep the day as it is, which can be conveniently divided into halves, thirds, fourths, fifths, sixths, eights, ninths, tenths and twelfths, as well as any multiples of those you like?