Having a AP in every room can be as significant boost if the walls impede the signal a lot. In fact we have one wall which is especially bad. Stand in front of it or next to it and reception from the front of the house is decent. Take one step back behind the wall and signal drops to less than 10%.

So having the 5-6 AP is not the problem, then shouting at max power is the problem. Especially “gaming” routers tend to do this.