The SI unit for time is the second (s). While it may be sensible to develop a new set of units for time using base ten, it would not be 'metric,' and integrating the new unit into SI would be non-trivial.
The main problem is that SI has many derived units related to the second. First of all, the newton (N) would have to go. The newton is the SI unit of force (much like the pound), and is defined as 1 kg*m/s2. It would be necessary to replace the second in this equation with the new time unit, which would create a new unit for force which is not equal to the newton. Then we'd have to get rid of the pascal (Pa), which is a unit for pressure. It is defined as 1 N/m2. This wouldn't be quite so painful because despite the fact that it is the official SI unit, most people use atmospheres or millimeters of mercury instead. This is very silly, but it's what people seem to do.
The next one to go out the window would be the joule (J), which is defined as 1 N * m. Although the second does not seem to appear in this equation, the newton does, and since we're tossing that, we need to also toss any other units based on it. Now we have to get rid of the watt (W), which is a unit of power - 1 J/s. Then the volt, a unit of electric potential, which is 1 J/C. Speaking of coulombs, (charge) either they go or the ampere goes. The ampere is a unit of electric current equal to 1 C/s, and there is some disagreement over which is the base unit.
There's more, but the point of all this is that a new time system may or may not be worth implementing, but it would be a much more complicated matter than advocates make it out to be. Changing any base unit would totally alter the metric system itself. Actually, you could change the unit for time without changing any of the derived units, but then you'd need to use weird conversion factors, which kind of defeats the purpose of SI.
IMHO, our time system doesn't really need changing. The thing that seems to bug people is not the second itself, but rather how it relates to minutes, hours, and days. However, these units are good enough for everyday use by non-scientists, and scientists don't use them anyway. Sure, the second might not relate to the day in a sensible manner (86,400 seconds per day), but none of the other metric units are based on properties of the planet Earth*, so why should the unit for time be? In any case, most chemists and physicists always record the time in seconds, so they don't need to care about how long a day is.
*I've gotten a couple complaints about this statement, but I stand by it and will attempt to justify it. The meter was originally meant to be 1/10,000,000th of the distance from the north pole to the equator, but in reality it is more like 1/10,018,800th. The meter is still fixed at its original length, however, so it is not based on an accurate measurement of the Earth, and furthermore it is now defined based on the speed of light.
The degree Celsius was based on the melting and boiling points of water at sea level, but the kelvin, an absolute unit, has 273.16 fixed at the triple point of water. While the unit size is contrived to be identical to that of the degree Celsius, it is not nominally based on it.
Finally we come to the Atmosphere. 1 atm is equal to the pressure at sea level. Well, I'll just say that this is not an SI unit, so it doesn't count.