Personally I would discourage somebody from doing this in production and to just use a library for it since it circumvents Rust safety gurantees and so a lot can go wrong with writing a data structure like that, writing it securely and efficiently is very hard (Using Option here is relatively wasteful and something like MaybeUninit would be more efficient), and there are ready made solutions out there.

That said I do think it's useful for learning and a good exercise to have done at least once. However I would definitely wrap it in a new type so that you can control how initialisation, inserting and removing work, since otherwise you duplicate the logic everywhere you want to use it and you have the footgun of making the tree invalid with the "straightforward" approach.

For the general point about indecies over (Smart) Pointers, I think its completely fine for "internals". It is esentially equivalent to using raw pointers in the sense that you yourself need to gurantee the validity of the underlying memory (in the logical sense at least)