This is a great point and I appreciate you pointing it out. Cross platform development is hard regardless of which part of the stack you're developing for. The reason development for the browser stands out for me is that when I build a web app I can control to a certain extent what environment the server is deployed in and then I don't have to worry too much about different platforms. However I have no control over which browser my user chooses to use and that can have a serious impact on their experience. An impact that I have to account for.
It's pretty easy to control, just detect which browser and throw up a screen saying that browser isn't supported or "use at your own risk." I don't see any distinction between cross platform support and cross browser support.
