This is great info for hatchery eggs you want in an incubator. But there might be some differences with eggs for a broody.
A clean incubator and a broody that takes a walk in the dirt every day is absolutely not the same.
I wash and refrigerate the very dirty eggs (rarely need to). The good ones are kept in a cupboard. Only in summer when it gets warm >25 C I refrigerate eggs if they are not eaten within 2 or 3 weeks.
Why keep eggs cool if there is no need for it? I only keep the formerly dirty and washed eggs...