The common phenomenological explanation of the forward active transistor operation is (e.g. in case of a NPN transistor) that when the base-emitter junction is forward biased holes can diffuse from the base side to the emitter side and electrons from the emitter side to the base side. Because the base is thin and there is an electron concentration gradient to the collector space charge region they diffuse in this direction and are then swept away to the collector by the space charge field.
This means the base current is just the normal hole current of the base-emitter diode and the collector current is just the normal electron current of the base-emitter diode. (Electron-hole recombination in the base neglected.)
This explanation would imply that when the collector is left open the whole emitter current is steered to the base, so the base current with open collector would be beta times larger.
From physics point of view (not electrical engineering point of view), why does this not happen? What impedes the electron diffusion even for large base widths when the collector is open?