The meter or the second are defined in that manner to actually make a primary standard accessible to well-equiped metrology labs everywhere. This way you don't have to make secondary standards that need to be periodically transported and compared to the primary standard. That was the way it was done before - with the Pt-Ir primary standard kilogram and meter bar kept in France, for example.
The astronomical unit seems pretty arbitrary to me. Gee, what's the chance that the Earth would orbit Sol at exactly 1.00000 A.U.? And since the Earth's orbit is actually an ellipse, we could even argue about the definition of an A.U. It's mostly the dimensionless numbers or ratios (like pi) that have deep significance for the way the universe works.