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.
But you might need to remove a given element that you have a pointer to in O(1), which a singly linked list will not do