In my experience, the rule at academic Biology US labs is that everybody brings their own laptop. Having said that, it is my opinion that there are two separate issues. 

The first issue/question is if it's fair for an employer to ask an employee to purchase their own work-related equipment. The answer is more complicated that it might seem at first glance. For example, there are tax implications, and the tax rules are not easy to interpret and/or apply. If your employer requires you to use a specific tool as a condition of employment, the employer is usually required to pay for it, or to have you buy it and reimburse you. Some employers use this as a loophole to pay for tax-free perks for employees, for example, computers, cells phones, cars, etc. There have been several high-profile criminal cases in the US press lately that centered around the use of "work-related" equipment as a way to avoid taxes. A computer is hard to classify as either business or personal, since it can easily be used for both. But my point is not to argue one way or the other, but that it's not an easy line to draw and that the university policy might have less to do with principle than to avoid complicated tax situations. Another issue is keeping confidential data on employee-owned computers, but that issue is not simple either and universities deal with it in many ways, e.g., having data management rules that apply to both personal and university-owned computers, requiring whole-disk encryption, or that student data be kept at university-owner servers and not as local copies. 

The second issue is if this a big deal a reasonable request, or a fight worth having. At least for the biologists I know, computer choice is very personal. People are either Mac or Windows, and a minority (myself included) are Linux-only diehards. Some people just use their machines for email, others are doing computationally-intensive tasks on them, the type of task that falls between what a mid-range computer can do and what you'd send to a cluster. And universities vary in their policies. In some places, every breathing person gets a computer on day 1 regardless of the actual job. For example, I once worked in a lab where a field technician, a person who never had to sit at a desk, got a computer assigned. She just set it up in the lab for everybody to use. But at that same place graduate students were never given a computer, even if the PI wanted to buy it with research money, the university objected citing tax issues, internal policies, NSF, etc. etc. At another place I worked, you could get a computer, but these were always the crappiest models available. At yet another place I worked, I was assigned a bare-bones laptop, which after 4 years of OS updates it became too slow to use. So I requested a replacement, and they gave me a used computer, identical to the one I had. So I went back and demanded a NEW computer, and they gave me a new (as in the box) 4-year old computer. Only at MIT did I get a brand new computer to my specs, but that was MIT. 

So what I urge to do is look at the overall compensation. For example, what are really big issues in the USA are health care costs, childcare costs, the cost of rent in coastal cities, etc. Consider your overall pay package. If the health insurance is good, the salary is reasonable, the lab environment good, the local rents are affordable, etc., then spending $900 on a laptop every couple of years is not a big deal. BTW, I quit my job at MIT, because the overall compensation was too low, so I moved to a much better job, and just buy my own computers. 

I used to get worked up about this being "unfair" of having to buy my own laptops for the benefit of my employer, but in light of the issues listed above, I have no problems spending my own money on the most important tool I use. This is also common in other workplaces, e.g., most car mechanics have to bring their own hand tools when getting hired at a shop, carpenters bring their own basic carpentry tools when joining a crew, hair stylists usually bring their own scissors, real estate agents buy their own cars, etc. This does not mean that these workers bring all of their equipment to work: mechanics don't have to bring lifts, carpenters don't have to bring Lulls, and stylists don't have to bring the chairs where clients sit, etc. In this same way, a biologist does not have to bring their own PCR cyclers, sequencing machines, or micropipettes, but they do bring their own computers.