I’m not saying that exclusives didn’t play a part entirely, but even when the PS5 was hard to get by it was still cheaper than the Xbox that were in stock (where I live).
Despite the low amount of exclusive games it would still be an easy pick to get a PS5 instead, if people decided to upgrade at some point. And since a lot of cross-platform/console games were still coming out on the old consoles for a while there was little reason to get an Xbox instead of a PS if they wanted a new console right then right there.