Why do we not use the SI system for distance in space? One of the closest stars to Sol is Alpha Centauri at 4.367 Ly according to wikipedia. Why do we not say that it is 41.343 Peta-meters rather? (4.367 Ly = 41.343 Pm) 
Why does Light-years or Parsecs seem to be the standard rather than SI?
 A: Light years and parsecs have been used since long before SI existed, so a lot of it is tradition.
But using light years also makes it very obvious how long the light has traveled to get here, and thus which era of the universe we are seeing the object in. Something that is 11 billion light years away dates from the era of early galaxies, for example. If you gave the distance as 100 yottameters instead, it would be far from obvious unless your listener was particularly familiar with distances on that scale.
For closer objects, parsecs are useful because they directly relate to the amount of parallax shift seen between opposite sides of the Earth's orbit. This is not so relevant now, but in the days when parallax was a standard method of measuring distance to astronomical objects, it was very convenient to be able to convert a parallax directly to a distance. (The name "parsec" actually comes from "parallax arcsecond".)
A: 
Why does Light-years or Parsecs seem to be the standard rather than SI?

In the solar system astronomy, the astronomical unit is much more widely used rather than meters for distance, days (86400 seconds), Julian years (365.25 days), or Julian centuries (36525 days) are used rather than seconds for time, and the solar mass is used rather than kilograms for mass. The latter is particularly problematic because of the uncertainty in the Newtonian gravitational constant G. Using the solar mass as the standard for mass rather than the kilogram eliminates this problem. One solar mass is the standard for mass throughout astronomy and cosmology.
The astronomical unit is only useful for solar system objects. The parsec (not the light year) is the scientific standard for nearby stars and galaxies. The reason the parsec is the scientific standard is because parallax is directly observable for nearby stars. A series of standard candles enable the use of parsecs as the unit of distance for stars and galaxies that are somewhat more remote. The distance in parsecs can easily be translated to light years for lay readers who may not have an intuitive grasp of what a parsec is. Expressing distance in some ridiculously large number of meters doesn't make sense, period.
For extremely remote objects, the concept of distance doesn't quite make sense. Redshift z is what is used in the scientific literature for extremely remote objects. This can be translated into the amount of time it took the light from those extremely remote objects to reach us, but there are certain cosmological assumptions that need to be made to perform that translation. The constants used in that translation are not perfectly known; they change as scientists improve their understanding of the universe. On the other hand, the observed redshift value is what it is.
Multiplying that time needed for light emitted by a remote object to reach us by the speed of light yields a distance value, but that value is highly suspect.
A: SI units are created for everyday life and therefore convenient to use in everyday life. The following sentences makes sense in modern human mind; "I live 300 meters away from here" or "My new boat is 35 meters long" or "I am bust now please call in 5 minutes". Moreover the calculations with these numbers are easy. If you hear someone saying "I drove 50 km Thursday and 35 km Friday" then you can easily calculate the total distance travelled.  
However, as science proceeds and we learn and care more about things in different scales, SI units become cumbersome. Therefore people create more convenient units to be used in different branches of science. It does not make much sense to use the same scale to measure the diameter of sun and size of a hydrogen atom or mass of proton and mass of an elephant or age of the universe and lifetime of an exited atom to relax.
