A finite routing realization, not an efficiency theorem

The proposition assumes availability of the endpoint computation. If geometrically local elementary implementation is also required, its layout and routing are additional costs. For example, after explicit lookup expansion, any finite one- and two-qubit gate list on $W$ wires can be implemented on a supplied nearest-neighbour line by moving operands together with SWAPs and undoing the move. This uses $O(W)$ extra gates per two-qubit gate, the same width up to declared scratch, and a serial schedule. It is a finite construction, not a polynomial-in-$n$ physical realization of an unrestricted oracle.

Any specified nonzero gate duration contributes to availability time. No null-arrival limit follows from this finite construction.