I think this is a good idea, and am always for things that increase privacy, but I wanted to clarify, in case you didn’t know, that it may not make a difference, and you can’t rely on small things like this to keep you anonymous. There are so many ways sites track you, using private browsing mode is very unlikely to actually make you anonymous on most sites. That’s not even what it’s for; it’s actual purpose is to keep your browsing private on your computer, NOT outside of it. Your ISP can still see everything you do, sites can still tell who you are via cookies, trackers, monitoring how you type and how you move your mouse, your IP, your browser’s and computer’s fingerprint, and so on. The only ways to actually ensure that you’re anonymous are to use Tor (best, but not perfect or foolproof) or a VPN (good, but many are flawed, free ones often monitor your traffic to monetize it/you, and there’s still fingerprinting, cookies, trackers, etc). I don’t know how anonymous/private you want to be, and stuff like this certainly doesn’t hurt, but you also shouldn’t have a false sense of security about it and should be aware of the reality of the situation so you’re not thinking you’re anonymous when in actuality you’re far from it.