Some do. In fact Microsoft is doing just this right now and many companies are supporting MS, including Google. Unfortunately, more companies came out AGAINST MS and in support of the current patent system. See: http://seattletimes.nwsource.com/html/microsoftpri0/20137856...
It is interesting to note that the companies in support of MS are largely in the tech sector, while those against are largely in pharma/agriculture.
Note, this case is about changing the standard of proof in patent cases to a "preponderance of evidence" rather than the higher standard of proof, "clear and convincing evidence". While it doesn't get rid of the patent system, it should make it easier to beat weak patents in court.
The story I usually hear is that there are two main groups of companies that are lobbying for changes to the patent law, but because of the different nature of their industries they have diverging goals for patent reform and have not been able to reach a compromise (thus the legislature is also unable to reach a compromise). On the one side are the consumer electronics and software companies, and on the other are the pharma and biotech companies.
Of course they themselves may have benefited from the current rules quite a bit too, but they still can benefit more with some changes to the rules that remove the chance for these leeches from sucking blood from them and the whole economy. (For large enough players, growth in the economy as a whole will also affect their growths and profits.)
Large corporations generally have both positive and negative impacts on everyone's wellbeing, but these patent trolls, who don't produce anything of value, only consume resources, are clear negatives.