You're not wrong, but anyone with the budget to buy both will (and even some without the budget, unfortunately) when there's enough exclusives. You state that 'most of the library overlaps', but that's my point. When enough of the library doesn't, when enough games are exclusive, suddenly you have two gaming consoles that don't compete.

For instance, take the Nintendo Switch. While attempts have been made to port over games to the console, its hardware is a limiting factor and the Switch has many exclusives. There's no shortage of people who own a Switch and a PS5.