The appropriate figure of merit is range and specific energy (i.e. useful energy stored per unit mass), and that IS a limitation, but range of up to 500 miles is feasible for pure electric using existing batteries and structure and aerodynamic efficiency tech. Double or quadruple that is possible with cleverness and more exotic approaches. Even long-haul is possible with certain approaches to pure electric flight (either lithium-air, which has just as high theoretical useful energy as something like gasoline, or staging).

The only way "large aircraft" or "high power" is a limitation is just the speed at which things can be certified. Large passenger aircraft cost billions to bring to market, so companies are super conservative about it. But this isn't a fundamental technical limit of electric flight.

[0]Technically, there are structural scaling laws which detract from efficiency as you get bigger, but they don't become strong until you're very large... And they're countered by perhaps even more important positive Reynolds Number scaling effects, i.e. your lift to drag improves as your scale increases.