Why the high degree of granularity?
Why not just let the extra seconds accumulate until they amount to an hour, then we just knock an hour off or add it to the time as required, like we do with Daylight Savings?
If the slowing of the Earth's rotation is proceeding at a constant rate, then that hour should be predictable enough to be able to program it into timekeeping systems, the way our computers recognise Daylight Savings and adjust the time automatically when it occurs.
Given that the rate of slowing is also very slight, we'd only need to do this every couple of decades or so in any event.
I'm sure there's scientific reasons for doing it as we do, relating to the timing of events and phenomena, but for that we could use a clock based on, say, seconds elapsed since the Big Bang, without worrying about other time periods like days or months or years.
OK, we don't know the age of the universe to that level of precision, but we could allocate an arbitrary value to run with until we do. We currently reckon the age of the universe at 13.82 billion years, based on observations by the Planck spacecraft.
For example, we could say this is the year 13,820,002,015 After Big Bang (ABB), at epoch 2000 AD there were 31,558,149.504 seconds per year, so Jan 1 2015 AD translates to 436,133,689,734,951,250.56 seconds ABB. Then scientists can take their time on that basis without having to worry about the slowing rotation of the Earth or other orbital anomalies.
Obviously, as our observation of the age of the universe becomes more precise, we can then update the scientific calendar as required.
Meanwhile the rest of the world, which functions on hours, days, months and years more than it does seconds, can live in peace with only an hour's adjustment every couple of decades or so.