Harry says in White Knight when walking into Anna Ash's home without an invitation that this leaves some of his power metaphorically at the door. The thing is that a fraction of Harry's power is probably still enough to win any fight against Anna and the same is all the more true when dealing with beings more powerful than him. For an example think of Cowl in Dead Beat, he was trying to become a god so he could kill the Senior Council though their best wards. If any level of threshold would provide better protection than those wards the Senior Council would be chilling behind those but they are not, they are behind the Merlin's wards which still are not enough to deal with an ascended Coil.
Now there are beings for which the limitation is much more severe, like the Black Court, but generally even the best threshold in the world will only cut down a faction of the intruder's magic, so the question becomes how much did they have to begin with?