What is the most common mistake in Pyramid?

Taking any legal pair as soon as it appears. Pairs that clear cards from opposite sides of the pyramid feel productive and open nothing.

Should I clear a King immediately?

Usually yes — it is a free move that can only help, and it opens whatever is underneath. There is no cost to it.

Why do so many Pyramid deals feel impossible?

Because many are. If a card is stacked directly above its only remaining partner, neither can ever be cleared. That is a property of the deal, not of your play.

Pyramid Solitaire Strategy — How to Win More Often

Pyramid Solitaire StrategyPyramid rewards counting and patience: dig downward rather than across, track which ranks are gone, and spend the stock last rather than first.