A "Minute" is a division of 60. "Second" comes from "Second Minute", which is a second division of 60.
"Decimal Second" is therefore an objectively absurd term.
If we use "day" as a base unit, we run into a bit of a problem. The subordinate units would be deciday, centiday, milliday, microday, etc. But There is no SI prefix for 100,000th, and 100,000th of a day serves much the same purpose as the second. We really need a unit about that size, so we either need the old "dimi-" ("decimilli") prefix, and create a new "cimi-" ("centimilli") orefix, or we need a different base unit.
We could use the milliday as the functional base unit: Call 1/1000th of a day a "chrone". Then we have a centichrone as 1/100,000th of a day (0.864 of a second), and a full day is a kilochrone.