Why transistor doesn't oscillate in this configuration?
Why would all of the current flow through Vce? Even if the transistor is entirely on (dead short), you still have LED voltage drop so you'd have LED voltage drop across 100k so you'd still have at least some base current. You are right to an extent that these two things will balance eachother out to some degree and find an equilibrium. Nothing here appears to cause any sort of oscillation though. 

Even if you removed the LED, instead of oscillating, the transistor would find some equilibrium point where the voltage Vc would be enough to support the transistor base being on to some degree.

Maybe you're having trouble with this idea because you believe transistors are like on-off switches? They're not. They're gradual turn-on/turn-off devices.