You can have signed apps and sandboxing without Apple being the sole arbiter of what you install. For example, Linux has multiple options available to solve this. Signed repos combined with SELinux, or flatpak, and snap all solve the same problem.
Signed app distribution won't solve this problem.
Chrome hides this as legitimate value to users - when I type out an URL on my desktop, I will get auto complete for it and shared history on my phone and my laptop. It's a trade-off.
It has nothing to do with signing.
Just because something is a solution, it doesn't automatically make it good. I can _at the same time_say that it is problematic that people die in the traffic _and_ loathe banning cars altogether.
Letting Apple act as the internet court might help on some problems. But letting a commercial entity act as legislative, executive, and Judicial power in the software distribution realm is simply not a good solution.
Something like this doesn't happen, and would not be acceptable, on a desktop computer.