Applications that operate in a browser still need to have semantically correct code. If the code is not correct then the chances of it rendering correctly in the browser are severely reduced.
Also, if the application that you are developing is for the world market, it needs to be as compatible as possible to give it a fighting chance. It will be faster too because the browser will have all the information it needs to render it correctly. Cognitively challenged people will have a better chance of being able to use your app if it is coded correctly. Screen readers will read out things in the correct sequence. Keyboard-only users will find that the tabbing order is correct. All these things are important for an optimal user experience, no matter who you are.
It is also worth remembering that, if your app is going to be beneficial to government organisations it will have to meet W3C guidelines to even qualify as a product that can be used. There are legal obligations and site owners have been sued for discriminating against people with disabilities that mean that they need to use a browser in a specific way.