It would rebalance on insert with O(log N) performance but chunky constant factor, keeping the ordering so access by index is also O(log N) with low constant fa

It would rebalance on insert with O(log N) performance but chunky constant factor, keeping the ordering so access by index is also O(log N) with low constant factor... Which is why usually you would use a red-black tree rather than a BTree, as it has much lower constant for insertion and access by index. However higher for traversal in order.