using a transistor or mosfet to power sim800 module

septillion:
But why do all this to save so little? The sleep current is 0,7mA max. Okay, it's not nothing but a single led draws at least ten times that.

700uA means you can't run something off batteries unattended for more than weeks
(unless pretty large batteries)
~10uA standby means you can run something unattended, battery powered, for years...
(assuming the standby current dominates and battery chemistry is low self-discharge)

There's a qualitative difference in something you only have to maintain once a year rather than
once a week...