The most common use of XOR that I'm aware of is in Adders, where it is 2-3 input. At the moment a half-adder takes 4 blocks to implement, and a full-adder 9, whereas were an XOR block available they would only take 2 and 5 respectively. In that scenario, a 1-only (not really)XOR would be perfectly fine. However, if the example was multiple corridor switches controlling the lighting system, it would be appallingly bad.Well, it isn't so much an XOR as it is a way to toggle a value whenever a switch is flipped. It's not actually useful for something like reading parity values.
Anyway, what is the purpose of 1-only XOR?
My argument for a 1-input only XOR was based on faulty logic: forgetting a) 3-bit truth tables, and b) 2-bit logic is chained gates. In other fields, possible, we may be able to to think of 'exclusive or' as implying mutual exclusiveness, 'one of', rather than 'either-or', since we are not restricted to only 2 states. I acknowledge that is a weak argument though, as I am moving into semantics.