In fact, it's already possibly (and easy) to obtain the un-anonymized browsing history of millions of people. I was part of a (journalistic) team that got their hands on a free sample from a company that offers "website traffic analytics", and which uses browser extensions as well as mobile apps as their main surveillance tools. The data set contained the complete browsing history of almost 3 million German Internet…
Companies don't have a monopoly on violence and complete control over you life as governments do, also, they are not unregulated or above the law - this company for example is probably breaking several laws. Spy agencies on the other hand, regularly break laws with impunity or have the laws rewritten to allow unlimited storage (as recently in the UK).
Governments are a much bigger worry when it comes to saving internet history as they have greater capabilities for capture and storage, and a simple policy change in 20 years could make everyone who visited a certain site a criminal liable to deportation or imprisonment.