Why cannot circuits like astable multivibrator, RC phase shift oscillator and wien bridge oscillators be used as inverters?
The power level of the usual applications of inverters is the main obstacle.

With power levels of, as you say, 100W, for example, the inverter must be very efficient, otherwise you would have two problems:


lots of energy (i.e. money) wasted into heat;
lots of heat to get rid of (or the circuit will cook to death), and this means massive (i.e., expensive) heat sinking and complex heat flow management (even with fans and, to the extreme, liquid coolant).


Even if the circuit is 80% efficient (which is more or less the minimum for actual inverters), you have to get rid of 20W of heat. And 100W inverters are not so big. Imagine what would happen for a 1kW unit: you get a 200W heater for free!

The circuits you mention are used for low power signal, less than some milliwatts usually, so even if they have poor efficiency, it is not a problem. I never calculated the efficiency of, say, a one transistor phase-shift RC oscillator, but I suspect it could be very low (less than 30%), since the BJT operates as a class A amplifier.

For more details about inverters' efficiency you can see this site.