If that's a specific use case you need to handle, it's O(1) again if you have a pointer to both the node to be removed and the previous node.
Whether it's more efficient to carry a second pointer around when manipulating the list, or store a second pointer in every list node (aka double linked list) is up to your problem space.
You’re assuming no other data structure points to the element. It may. Example: implement a cache.
Each element is: key, value, linked list node for hash table bucket, linked list node for LRU. Hash table to look up element. Element is both a member of hash table and of linked list. Linked list is used as LRU for feeling memory when needed.
LRU never traversed but often needs removal and reinsertion.
Stop!
If you are using a doubly linked list you (probably) do not have to, or want to.
There is almost no case where you need to traverse a list in both directions (do you want a tree?)
A doubly linked list wastes memory with the back links that you do not need.
A singly linked list is trivial to reason about: There is this node and the rest. A doubly linked list more than doubles that cognitive load.
Think! Spend time carefully reasoning about the data structures you are using. You will not need that complicated, wasteful, doubly linked list