Finance person here in the US who has seen the finances for hundreds of PIs before and can shed some light on this "wealthy" comment. 

First of all, no PI is required to fund anything, period. They can have $20M in discretionary funding and still not want to spend it on laptops. That is their choice. The reasons to do this can be numerous, and sometimes it can be about setting precedents.  It can also be because of someone like myself saying no. I personally refuse to issue postdocs a laptop because they are two-year appointments, and our IT policy depreciates laptops over 4 years. This means we get stuck with said laptop and no one wants to use it. The PI doesn't want to keep track of it. How do I know it won't walk away? Once we know it walks away, we would have to notify IT to remote wipe the PC.  How do you think that would go over?

How can I enforce these policies?  My personal solution has been to offer a one-time taxable bonus of $1,600 and they buy their own device. Our IT dept is required to lock the device down due to our data security policy. You have to know your own institution's rules to know what is possible. You could then try to approach your PI based on the computing policy, but again, the discretion is with the PI, and no means no. PIs need to plan carefully to spend money over decades to ensure they do not have funding cliffs and have to terminate all their staff. What looks like a lot of money today can dry up within only a few years. Even if your PI seems agreeable, there can be a research administrator telling them this is a bad idea for various reasons that do not directly impact you. Another answer here covered some examples of policies that make some institutions squeamish. 

As for sponsored funding, many sponsors explicitly do not fund general use computers. These costs should be picked up by the institution as part of their "facilities and administration" or "indirect" costs. I have only written computers into a budget a few times because they are computation focused and require specific GPUs to accomplish the scope of work. When researchers try to push a computer purchase on me (particularlyon sponsored funding), I ask things like, "so you can guarantee you will never check your email, be on social media...?" Suddenly this device is not only to benefit the grant, it is in fact a somewhat personal device. This is why I came up with my solution mentioned above for PIs who want to issue devices.