What would be the main advantages of constructing an astable multivibrator with two CMOS inverters?
They are simple and often can be implemented using unused inverters in an existing package that has six of them, so more economical than, say, adding a 555 for the purpose.
Yes, there will be some parasitic capacitance.  That is true of all components.
An astable multivibrator can be done with a single inverter: a schmitt trigger type.  Two could make a latch, of sorts.