Quote: The truly scientific approach would be to declare the day to be 86400.002 seconds, and lengthen that number over the centuries, would it not?

Not.

The length of an earth day is not stable, nor is the increase stable. The most important fact is that it is not predictable. Would that it were. If your universal day standard was adopted, there would still be a need to add or subtract leap seconds over the years as the earth matched or missed the estimate.

The tiny tiny change in the length of an Earth's day varies enough to matter (to some people) each day. The nuclear missiles the ballistic missile submarines fire use a star correction in flight to update their targeting. THey need to know precisely where that star is in order to determine precisely where they are in reference to their programmed flight, to calculate where their intended target is and what they need to do to get there.

There are observatories that measure the exact length of a day, and provide a correction value for the UT, called UT Correction, or UTC. It's entered in the computers for the missiles twice a day. UT plus (or minus) UTC equals real-real UT.

The purpose of implementing a leap second to the UT is to reduce the size of the UTC. The smaller the error, the more accurate the correction will be.