This is 100% something that can be fixed by the browser. Package updates don't change existing files but rather create new files and update the filesystem to point to them. All it takes to not need a restart is to keep file handles open for all needed resources and forking from such a process instead of exec()ing new ones. Not entirely trivial for applications as monstrously complex as browsers but hardly comparable to other challenges they need to solve. It's only because they can control the update process on the OS they care about (Windows) that they don't bother.
