Each time I'm too lazy too cook I think it'd be cool to be able to just plug myselt into an outlet. Yet I know it is not possible - I need amino acids and a lot of other stuff that electricity can't replace.
Can some simple organism live on electricity alone or is it just fundamentally impossible?
No; the problem is, as you pointed out, that no organism will manage to multiply, grow or even sustain itself without absorbing matter to create new cells and fill metabolic losses.
Even photoautotrophic organisms which get energy from light (which is in fact an E-M wave, so pretty close to electricity) collect matter from the environment -- plants for instance seem to grow out of nothing, but in fact gather significant part of their mass from atmospheric CO_2.Tweet