In astronomy distances are generally expressed in non-metric units like: light-years, astronomical units (AU), parsecs, etc. Why don't they use meters (or multiples thereof) to measure distances, as these are the SI unit for distance? Since the meter is already used in particle physics to measure the size of atoms, why couldn't it be used in astrophysics to measure the large distances in the Universe? 

For example:


The ISS orbits about 400 km above Earth.
The diameter of the Sun is 1.39 Gm (gigameters).
The distance to the Andromeda Galaxy is 23 Zm (zettameters).
At its furthest point, Pluto is 5.83 Tm (terameters) from the Sun.


Edit: some have answered that meters are too small and therefore not intuitive for measuring large distances, however there are plenty of situations where this is not a problem, for example:


Bytes are used for measuring gigantic amounts of data, for example terabytes (1e+12) or petabytes (1e+15)
The energy released by large explosions is usually expressed in megatons, which is based on grams (1e+12)
The SI unit Hertz is often expressed in gigahertz (1e+9) or terahertz (1e+12) for measuring network frequencies or processor clock speeds.


If the main reason for not using meters is historical, is it reasonable to expect that SI-unites will become the standard in astronomy, like most of the world switched from native to SI-units for everyday measurements? 

In addition to the answer provided by @HDE226868, there are historical reasons. Before the advent of using radar ranging to find distances in the solar system, we had to use other clever methods for finding the distance from the Earth to the sun; for example, measuring the transit of Venus across the surface of the sun. These methods are not as super accurate as what is available today, so it makes sense to specify distances, that are all based on measuring parallaxes, in terms of the uncertain, but fixed, Earth-Sun distance. That way, if future measurements change the conversion value from AU to meters, you don't have to change as many papers and textbooks.

Not to mention that such calibration uncertainties introduce correlated errors into an analysis that aren't defeatable using large sample sizes.

I can't speak authoritatively on the actual history, but solar system measurements were all initially done in terms of the Earth/sun distance. For example, a little geometry shows that it's pretty straightforward to back out the size of Venus's and Mercury's orbit in AU from their maximum solar elongation. I don't know how they worked out the orbital radii of Mars, etc, but they were almost certainly done in AU long before the AU was known, and all of that before the MKS system existed, let alone became standardized. 

For stars, the base of what is known as the "cosmological distance ladder" (that is "all distance measures" in astronomy) rests on measuring the parallax angle:
$$\tan \pi_{\mathrm{angle}} = \frac{1 AU}{D}.$$
To measure $D$ in 'parsecs' is to setup the equation so that the angle being measured in arcseconds fits the small angle approximation. That is:
$$\frac{D}{1\, \mathrm{parsec}} = \frac{\frac{\pi}{180\times60\times60}}{\tan\left(\pi_{\mathrm{angle}} \frac{\pi\, \mathrm{radians}}{180\times60\times60 \, \mathrm{arcsec}}\right)}.$$
In other words, $1\operatorname{parsec} = \frac{180\times 3600}{\pi} \operatorname{AU}$.

Astronomers also have a marked preference for the close cousin of mks/SI units, known as cgs. As far as I can tell, this is due to the influence of spectroscopists who liked the "Gaussian units" part of it for electromagnetism because it set Coulomb's constant to 1, simplifying calculations.
