I agree with @matklad that doubly-linked lists are most of the time not what you want.
This premise begs the questions: When do you actually want a doubly linked list? And does that happen enough for them to be in std?
The only case in which I would personally consider a doubly-linked list over similar data-structures (singly-linked lists, double-ended queues, …) is when I need O(1) splice as an algorithmic building block (VecDeque and singly-linked lists have O(n+m) splice). Are there other cases you can think off?
This is an extremely niche requirement, and I don’t personally think it is enough for putting a collection in standard. Even if I would have this requirement for a problem, a VecDeque is probably much better for small Copy types and not-unreasonably large lengths because memcpy is way too fast`.
Also, the current LinkedList in std does not help me here, because it can only do O(N) splice. I don’t even know if the doubly-linked lists in crates.io would help me here, because the ones based on Cursors do not let you have a reference to multiple nodes of a list, while you are splicing into it (even though splicing does not invalidate references to other nodes). So depending on what the algorithm requirements are, one might well be completely out-of-luck here.
I think that solving all these problems is really interesting, but it appears to be also in a very research-y state. Whether LinkedList can be upgraded in a backwards compatible way to solve these issues remains to be shown, but if that can be done we can always un-deprecate it later. We can’t ever remove LinkedList from the std library anyways, but in its current state, it appears to be a completely useless collection to me.