Therein lies the problem. PoP from models are created from QPF. The more QPF the higher the PoP (to a certain extent, it's not like you need 5 inches to get 100% PoP). So even if a model is spitting out a lot of 0.01" amounts, that will translate to a low PoP. And if you blend a bunch of models with 0.01" in different locations, the PoP can go even lower.
So you manually need to increase the values. That's usually the failure point in the forecasts.