Is a kitchen island always worth adding?

Only if the clearances survive it. You want at least 1,050mm of walkway on every side that is used, and 1,200mm on the side where a dishwasher or an oven door opens. Below that, two people cannot pass and the room feels smaller than it did before. In practice a kitchen narrower than about 3.6 metres rarely takes an island without something else suffering. A peninsula gives most of the worktop and seating benefit in a room that cannot spare the walkway.