I don't know the precise details of how deques are implemented in C++, but given the most popular stack overflow explanation of them, some immidiate pitfalls are that the T* map itself sounds unbounded and if each chunk allocates only a fixed constant size it's probably horrible for fragmentation or overallocation. The indexing also seems dependent on division.

With this power of twos approach you can't really truly delete from the front of the array but the amount of pointers you store is constant and the memory fragmentation is better. (Though OP never claimed to want to support deque behavior, it shouldn't be that hard to modify, though indexing seems like it has to go thru more arithmetic again)

I haven't used OP's array, but I have been bit plenty of times with std::deque's memory allocation patterns and had to rewrite with raw arrays and pointer tracking.