Microsoft does indeed charge computer makers a royalty if they sell systems with their software installed. Damn them for wanting to get paid for their products! Anyway, they've long charged the same price for a MS operating system regardless of whether it comes with or without the IE browser. In fact, the browser capability is built into the OS in such a way that it can't easily be removed. That doesn't precude anyone from installing Netscape, Opera, or any other browser.

The question about integrating a browser into the OS is a basic one. First of all, what constitutes an OS? This question is fundamental in evaluating the Microsoft case, so it helps to understand the history of the subject. In the earliest days, computers didn't have much in the way of an OS at all. Programmers had to write their own routines to handle things like memory allocation (there wasn't much to allocate back then), communications with I/O devices, etc.

Here's a Jerry Pournelle column from 1999 about the Microsoft decision. He points out how the decision was based on a flawed understanding of the computer industry and inaccurate history. Pournelle has been a computer columnist at Byte since the late 1970s so he's been around about as long as personal computers and saw most of the industry's history unfold firsthand.
Over time, computer vendors developed standardized routines to handle these functions and sold that with their computers. In a sense, this represented some of the earliest reusable code. Over time, an OS came to be seen as a standardized set of services that applications programmers could use.

As the technology evolved, the standard set of services that constitute an OS expanded. For example, hard drives tend to become fragmented over time, so defragging utilitity programs were developed to perform this function. Some OS vendors bundled defraggers into their product while others left that function to 3rd party vendors (Microsoft didn't include a defragger with any of their OSs until somewhere around MS-DOS 5 or 6). Other examples of things that came to be bundled with OSs include built-in networking capability (Windows for Workgroups 3.11), Graphical User Interfaces (MacIntosh, et. al.), and even browsers.

Microsoft wasn't the first to bundle a browser into their OS. IBM OS/2 (half an operating system?) 3.0 Warp did that in 1984 long before Microsoft did the same. Apple has included browsers with their operating systems for years now.

One advantage of having this capability bundled with the OS is that the application programmers know the end users will have certain functionalities on their computers. For example, I've used the MAPI (mail API) interface in some of my programs. I don't have to wonder what kind of email program the user system might have installed. Other capabilities like DAO, ADO, ODBC, etc. also come in useful in my programs.