I think you're being needlessly dismissive of how hard a problem it is. There are legitimate use cases for capturing mouse position. You could certainly make a secure browser, but you're also going to strip it of much of the functionality that we enjoy today.
The problem doesn't exist because people just aren't paying attention to security, or because the entire architecture of the web is flawed. The problem exists because it's a damn hard problem to deliver arbitrary executable code to clients on demand and let them run it and do useful things with it without compromising security and privacy. The browser vendors have really stepped it up in the last few years, and it takes a very narrow view of the web to see otherwise.
The problem doesn't exist because people just aren't paying attention to security, or because the entire architecture of the web is flawed. The problem exists because it's a damn hard problem to deliver arbitrary executable code to clients on demand and let them run it and do useful things with it without compromising security and privacy. The browser vendors have really stepped it up in the last few years, and it takes a very narrow view of the web to see otherwise.