Why didn't they tidy up this mess when they replaced feet, yards and miles with meters, ounces, pounds and short and long tons with grams and pints, quarts and gallons with liters?
Basically because while replacing these were all a question of taking an "arbitrary" standard and replacing it with another, changing our system of timekeeping would have to fit with the natural phenomena of days and years. Since the relation between these two, by celestial law, is 365.2421 days per year, a system which only operates on multiples of ten was not a real option.
Timekeeping remains the only area of meassurement where the relation between units is not a simple multiple of 10. This causes few problems except the difficulty in converting between the popular km/h and the scientific m/s and occasional mistakes when going from minutes to hours to days to years.
The second will probably stay with humankind as long as there are scentists left because of its place as one of the non-derived SI units, and the 24 hour "day" might survive humankinds migration into space. Experiments have shown that 24 hours isn't perfect, and we might not go to space, and if we stick around for long enough here on earth we'll have longer days, but that's another story.
There was an attempt in post-revolutionary France to introduce 10 hour, 100 minute clocks and 10 days weeks, but unlike the meter, liter and gram, this did not succeed. And lately the Swiss watchmaker Swatch has had some success with it's "Beat" (tm?) watch which divides every day into 1000, you guessed it, beats. I don't know when they came up with this, but I had a kiloklock java applet on my homepage a couple of years before I'd ever heard of Swatch Beat so if they try to claim I stole their idea, I'll laugh at them.
So basically my new system has no scientific value, but it's better than Swatch beats because I'm not trying to move the accepted main meridian from Greenwich to Bern, and because counting days opens up all sorts of amusing possibilities. The decimal date is based on days, an unnamed unit (not beat) equal to a milliday, and a point zero equal to 00:00.0 1903.07.13 UST. July 13th 1903 is day zero, the first day in my decimal date system. I chose a date at random, and July 13th 1903 has no significance to me.*
*Even though, at a later point, the birthdate of T&ATCA was set to July 13th 1991.