There are historians who have looked at individual corporations. The two places where this is common is the history of business, where the practices of a single big player can cause massive changes in the way the economy operates at times (e.g., Lewis Ranieri and Salomon Brothers and the mortgage-backed security, or the South Sea Company and its bubble, for example). The other place is in the history of technology, where there have been significant technological/industrial/governmental trends associated with major industrial firms, e.g., the DuPont corporation (David Hounshell, Science and Corporate Strategy: Du Pont R and D, 1902-1980), or the Germany chemical industry (BASF, Bayer, etc., which pioneered a ton of important interactions), or even the specific management styles of major military-industrial contractors (e.g. Thomas P. Hughes work on Convair and Project Atlas in his Rescuing Prometheus). There are, indeed, histories of IBM that frame it in different and very specific ways (Edwin Black's IBM and the Holocaust is perhaps an extreme version of that). In my own work I have spent a lot of time with the history of one small Michigan company (KMS Fusion) where the specifics of the company and its main actors are very important to the unfolding of a much larger story about nuclear technology in the United States (in the 1970s, they tried to develop, and patent, a new form of fusion reactor that the government deemed used classified technologies, and, unusually, they fought the government on this, which created all sorts of havoc). There are even some big, popular books about some of these companies, e.g., Gerner's The Idea Factory which is about Bell Labs (a corporate research laboratory), which was a bestseller.

So I'm not sure if it isn't talked about much. Business history is a field of history, has its own conferences and professors, and is often split between historians and economists and people at business schools. It definitely has its "tendrils" into other fields of history, like the history of science and technology (which is what I know the best, so I may over- or underestimate its influence elsewhere as a result of my own exposure biases). The main difficulties of doing this kind of work are that business archives are often closed, destroyed, or otherwise inaccessible — if the business is totally out of business, then they might just be gone, if they're in business, they are often tightly controlled for fear of negative publicity or liability (viz. my example about IBM and the Holocaust). Businesses sometimes employ historians to write their own internal, institutional histories (History Associates is a company that provides these services) but such histories are necessarily a bit self-serving and warped by the patronage (which doesn't mean they are bad, it usually just means they are boring).

But yes, such work exists, has existed for awhile, still exists. There is, for example, an annual Business History Conference; you can see the kinds of work that are presented on their most recent conference program. (Apologies for linking to a cached version of the page... their site seems to be having some technical issues at the moment.) Most of the papers seem larger in scope than individual corporations, but some are not (e.g., there is one that seems to be entirely about practices of the Eastman Kodak Company, which is one of those companies of sufficient importance and size to definitely attract a historian's attention).