How do I use it on my desktop or laptop then? What if I switch browsers on my phone? What if I get a new phone? What if I change from android to iOS or visa versa? What if I need to log into the site on my Wii U's browser?

So if I drop my phone to the toilet, I will forever lose access to everything? Since the vault is on my phone.

Not always. And which vault? There can be multiple on a given device. This isn't some hypothetical 'mollify the user's worries' question, this is an important practical question of what do they need to worry about losing access to. Trust me when I say that most users I have talked to have absolutely no idea about this, and usually only find out when they've already lost them.

Great, what happens if I lose my phone?