If you want to use an application, then why don't you download and run an application? You will have a better experience running an application on desktop instead of running it on the browser.
Write once run anywhere. Nothing else comes close. A lot of web applications simply wouldn't exist on your platform if they were forced to be native applications.
Except now replace "platform" with browser, and you have the exact same dilemma as if we still made desktop applications.
It's sad how many "web apps" (and even more regular sites) only work in Chrome - try using Firefox or any non major browser, and quite a lot of the web simply doesn't work.
Hardly the same. Desktop applications are still much more time-consuming to make. The differences between desktop platforms is on another planet compared to the differences between browsers, especially the difference between Firefox and Chrome, especially when you consider mobile.
Because the web is a revolutionary application distribution platform. It is a better platform in every way except that some things that should be applications are still behaving like websites (and vice versa) and that it is harder for developers to target than native platforms. But as a user, I don't care at all whether it is harder for developers.