Was it ever considered to optimise a jet to normally operate with one engine shut off?
I can think of one example: the Hawker Siddeley Trident 3B.
This had a fourth, small engine buried in the tail, which was only used during takeoff. They did this because it was cheaper than redesigning the aircraft for different engines.

Since the Spey 512 was the last of the Spey line, extra thrust would be difficult to obtain. Instead of attempting to replace the three engines with a completely different type, which would have been difficult with one engine buried in the tail, Hawker Siddeley's engineers decided to add a fourth engine in the tail, the tiny Rolls-Royce RB162 turbojet, fed from its own intake behind a pair of movable doors. The engine added 15% more thrust for takeoff, while adding only 5% more weight, and it would only be used when needed. BEA accepted this design as the Trident 3B, and ordered 26.