Personally am asking myself what the benefits of the BSD clause compared to a more restrictive license are. The only reason I personally can see is that they want to have to option to close the browser themself in the future.
Yup. All licensing is about brokering control. The only license that grants true freedom is no license, i.e. public domain. Everything else is a “where’s the control” shell game.
Sadly, that's not how it works; opting out of the copyright game is a lot harder than it should be. "No license" means all rights reserved, and even a public domain dedication is invalid in certain countries.
Your best bet is to put your code in the PD and provide a fallback maximally permissive license in countries with insane legislation where that doesn't work (e.g. Germany). The Unlicense notably does this, though lawyers seem to hate it for various reasons.
Alternatively, you can use licenses like 0BSD/MIT-0 which are PD-equivalent, but you technically retain copyright, so it should work in aforementioned countries too.