I'll note that in the US, it would be extremely unusual if a person starting a post-doc, or even doctoral studies, or maybe even secondary education, didn't have their own laptop already.
It would be different if the lab specified a system that a new employee were required to purchase on their own, but having a system of the user's choice (and at their expense) wouldn't seem unusual. In fact, the opposite would be unusual here.
For international students, especially those coming from a quite different economic system, it might be a strain and a lab would be wise to provide assistance for such students. But it would probably imply lack of choice in the characteristics of the system.
So, to be explicit about your headline question, it is probably unusual to ask a new postdoc to purchase a system because the assumption would be that they already have something suitable.