One reason could be that large number of users of web have no real power to set up their operating system to use their preferred DNS server (e.g. non-technical employees in many big corps). The present-day OSes are designed to favor the administrator and to restrict the users.
> (e.g. non-technical employees in many big corps)
IMO, employees should be using whatever their organization has configured for them -- not whatever they wish.
A "regular user" changing the DNS servers on his work PC (joined to an Active Directory domain) to 8.8.8.8, for example, WILL run into problems at some point. They say they have workarounds for this but I think it's safe to say that bugs will likely be found. In the meantime, things will be broken for those users.
Moving this setting into the web browser (where it likely CAN be changed by a user) is not the proper solution.