I think there are some legit cases / reasons to prefer linked lists:
Reason 1:
As others already described, insertion and deletion operations perform fixed in O(1) time for linked lists. This might be a significant advantage depending on your problem.
Reason 2:
You can do things with linked lists that you can't do with arrays. This is due to the nature of a linked list -> every list entry has references to its follower (and predecessor if it's a double linked list).
Example1:
If you have a linked list of items, you could store a reference to a "currentItem" in a variable. If you need to access the item's neighbors you could just write:
curItem.getNext();
or
curItem.getPrev();
Now, you could argue that you could do the same with arrays while curItem is just the current Index. Basically this is true (and in most cases I would use that), but remember that in javascript it is possible to skip indices. So if your array looks like this, the index-method would not work as easily as thought:
myArray = [];
myArray[10] = 'a';
myArray[20] = 'b';
If you find yourself in that kind of situation, maybe a linked ist is the better choice.
However, if you need random access to the data (which is more seldom than it seems in most cases) you would go with arrays almost every time.
Example2:
If you want to "split" your list into 2 separate lists, this would also be possible O(1) time. With arrays you'd need to use slice, which is more imperformant. However, this is only an issue if you work with large datasets and perform this operation often. 20 repetitions of slicing of an array of 10 million strings took about 4 seconds on my machine, whereas the separation of one list into 2 took <1 second (providing you already have a reference to the list element where you want to start the separation of course!).
Conclusion:
In some cases you would benefit from a list's nature and it's performance. In some cases, you would suffer from it's imperformance (inability to randomly access multiple data).
I've never used a list in javascript, but similar structures like trees or graphs are used for data representation (in both backend and frontend javascript). So analyzing/learning list implementations in javascript is a good idea for more complex structures.