ReverseEMF:
For a switch, the beta is in the lower ranges -- typically 10. For, applications in the active range, the beta is higher. It's like an Op-Amp. The beta rating of a transistor is like the open-loop gain of an op-amp. And the functional beta of a transistor circuit is is like the gain in an op-amp circuit, programmed by the resistor network.
I repeat, beta is the small signal current gain, its nothing to do with operating a transistor at saturation, and
its measured in the standard forward region of operation.
At saturation the base collector junction is forward biased, there is no transistor action in the standard sense
as the collector repels charge carriers from the base rather than attracting them. The current flows because
the density gradient of charge carriers is extreme(*), and carriers from the emitter have a better than evens
chance of diffusing to the collector before interacting with the base electrode. In fact usually 90% chance or
so.
In normal transistor action the emitter carriers just have to diffuse to near the base-collector junction, rather
than all the way to the collector contact. The reverse biased base-collector junction then attracts them across
very efficiently.
(*) The density of carriers in the emitter is about 10,000 times higher than the collector, the base is intermediate.