The fact that Google is expected to equally promote its competitors from its own website just goes to show how strictly is watched. In the website for your browser do you promote other browsers? No, and nearly nobody does this. But Google Search is expected to be fair to all and it is held at much higher standards than others.
And what would you upload to your website??
You don't need a server to steal data, especially in your case with a handful of users. It would be nothing hard to open a backdoor, and then from your computer to have access to the systems of anybody currently online who has installed your browser. You claim that you hacked Youtube, but for something way simpler you are trying to present it as impossible And if you wanted a server, what would stop you of having one? Sure you can say that you will not do such thing, but why would anybody believe you when you are shown to be both a liar and somebody who doesn't mind violating the law?