Anchors aren’t emergency brakes. Especially when ships get that big. What anchors mostly do is reduce (notice REDUCE) how much storms push the ship around. Most ships never even drop anchor anymore, they just aren’t that useful.
I recall reading (or viewing) that in many situations the anchor doesn't actually play a part in controlling the position of the ship. Instead it is the weight of anchor chain dragging on the sea floor that dictates how much the ship can move.
As a result, when the current direction changes on an anchored ship, the ship has to be prepared for motion as the ship traces a path over the anchor chain.
I think a ship can drop one anchor as it drifts in the current until it has let out a lot of chain. Then the ship can drop another anchor and take up some of the chain on the first anchor while letting out chain on the second anchor.
In its final position the ship would have to drag one or the other chains in order to move.
Freeper sailors feel free to comment.