What limits the maximum allowable current of a power LED?
One of the things that determines the LED lifetime is the junction temperature (the temperature of the LED die inside the package). Then it's a matter of how fast you can remove heat from that, given the thermal resistance between the junction and the pad where the heatsink attaches (upon which you have no control, and which may be lower for larger LEDs).

Some manufacturers have published data on temperature and current vs. lifetime which shows that indeed if you accept some reduction in lifetime and have proper heatsinking you can drive their LEDs at 2x the rated current.

See for instance the OSRAM Dragon reliability information. Note how the lifetime drops smoothly from 100,000 to 20,000 hours with increasing current/temperature and then suddenly to 0 hours when you exceed the maximal temperature (fig. 5). Note also how this depends on the LED color (fig. 5 vs fig.7), with blue/green/white LEDs much more fragile than yellow/red LEDs.