Your reasoning is not wrong, in that it takes additional energy to reduce metals like Na and K that are highly electropositive. This is the preferred method to extract these metals, though, because alternative methods are far more expensive.
For example, the first attempts to extract aluminum (or aluminium, if you prefer) by Ørsted, Berzelius and Wöhler between the 1820's and 1845 reacted potassium with aluminum compounds. The metal thus produced was costly, valued more than gold, even though it was neither pure nor useful. King Christian X of Denmark had a crown made of aluminum! In 1854, Deville brought down the cost to that of silver by using sodium instead of potassium... still rather pricy.
Paul Héroult and Charles Hall made innovations in 1886 that made electrolytic production of aluminum practical, so that now the cost is low enough that aluminum foil is considered a disposable (though better recycled) commodity.
With plentiful electricity, the cost of producing aluminum has dropped to ~US\$2/kg, and electrolytically produced sodium is ~US\$4,000/tonne.
Less electropoisitive metals are produced electrolytically where there is an economic advantage or to provide high-purity metals. Copper is a good example, because high-purity copper is a better conductor of electricity, so less metal is needed to make a wire of sufficient capacity, and because small amounts of precious metals such as gold and silver are recovered from the electrolytic sludge, helping to defray the cost of re-refining.