HTTPS and SSL certificates are primarily used for encrypting the connection, thus protecting your data from snooping and modification in transit. They are not actually that useful for authenticating identity. Users tend to simply ignore the padlock icon, which is why Chrome is moving away from an affirmative security display model (which users don't pay much attention to) to displaying prominent warnings for insecure or hijacked connections, which users do pay more attention to. SSL certificates' inability to properly authenticate identity is also why many of the largest tech companies in the world do not even bother with EV certificates (e.g. Google, Amazon, and Facebook for starters).
In order to fully establish identity and provide strong authentication, you would need a much stronger centralized system. Additionally, browsers would need to refuse to make connections to endpoints not authenticated through this system, otherwise you'd have the same kind of lackadaisical user response as we see now to the padlock icon. I don't think anyone present here wants anything like that, and I'm sure that if we were proposing such a walled garden vision for the Internet, the responses would rightfully be much more negative. Instead, we just want everyone's connections to be encrypted.
As for some of your other points, having a strong, short, memorable domain name is good for overall Web security and does help cut down on fraudulent apps and the other problems you've identified. To give you one example, I recently saw an ad for an app called "Curb" (it's a yellow tax ride-hailing app). Out of curiosity I wanted to see more information about it, but there was no domain name on the app; it simply said "Download the Curb app". So I searched the app store for "Curb" and there were dozens of apps with that name, many of them clearly imitators. The best "security" measure was trying to remember what the app's icon looked like.
Now imagine that that ad had instead said "Go to curb.app to get our app", and that said site had prominent links to mobile app stores. That's taking advantage of the global uniqueness property of domain names to guarantee that I won't be tricked away by a scammer. "curb.app" is short and memorable, gets users to the right place, and because .app is a fresh namespace, is still available. Good luck getting any domain name close to that good on .com. .com is fully mined out, and any good names that are available are being sold for minimums of tens of thousands of dollars by squatters and resellers.
I'll be talking about these issues and more in depth at I/O, if you'd like to watch/stream it: https://events.google.com/io/schedule/?section=may-8&sid=7ac...