Why do diode datasheets list a maximum forward current instead of power?
When forward biased (conducting), a diode only knows about the current passing through it.  It doesn't know what the voltage of the circuit is.  The power the diode has to dissipate is its forward voltage times the current - circuit voltage doesn''t come into the calculation at all.
When the diode is reverse biased (not conducting) it does know about the circuit voltage, or rather the reverse voltage that is applied to it.