The reasons aren’t worth listing because they’re all known but here we go
You need to use linux shell to get anything done.
There, that’s the reason.
Linux will never be popular until you can do everything, and I mean, everything without entering a single command in a terminal.
You are overstating how much you need the terminal a bit. You can most certainly install and update software without the terminal. I get your point, but it's not 2006 anymore.
On which distro/s can I install all package types without opening terminal once?
Have you used Linux lately? You can do this in any distro with a modern desktop manager. Discover in KDE Plasma, Gnome Software, and similar in other desktop environments are installed by default in the DE and have been for like a decade.
You can install every native UI application and every Flatpak (or Snap) in every distro that ships with GNOME or KDE without opening terminal once. Not sure how the software center works for others but I'm sure they do the same.
Fedora, Ubuntu, Debian, Mint and many more. They all do it like this.
Need to install more than UI applications? Install dragora/Synaptic whatever GUI comes for your package manager. Not like you really need to do this because the average person only cares about the UI applications.
As someone else has said, on distributions that go for ease of use, the terminal isn't really needed.
However, I do consider it a convenience feature even for users who are not savvy with it: You can either troubleshoot an issue by giving instructions like "Open application X, navigate to Option, open Tab, press Button, then enter Text, hit OK and repeat for each" or "copy and paste this command into your terminal". The amount of work on both sides is likely lower plus there's less room for error.
You would have to Give SUSE / OpenSUSE a try. It has Yast2-GUI so everything from setting up a samba share, ftp server, to kernal tweak, system services, and boot setup can be done entirely in the GUI environment. Very similar to how the older Windows Control Panel looked. Also One-click install for rpm files. Oh and system rollback if you blow up the system, no command line fixes needed.
The reasons aren’t worth listing because they’re all known but here we go
You need to use linux shell to get anything done.
There, that’s the reason.
Linux will never be popular until you can do everything, and I mean, everything without entering a single command in a terminal.
You are overstating how much you need the terminal a bit. You can most certainly install and update software without the terminal. I get your point, but it's not 2006 anymore.
On which distro/s can I install all package types without opening terminal once?
Have you used Linux lately? You can do this in any distro with a modern desktop manager. Discover in KDE Plasma, Gnome Software, and similar in other desktop environments are installed by default in the DE and have been for like a decade.
You can install every native UI application and every Flatpak (or Snap) in every distro that ships with GNOME or KDE without opening terminal once. Not sure how the software center works for others but I'm sure they do the same.
Fedora, Ubuntu, Debian, Mint and many more. They all do it like this.
Need to install more than UI applications? Install dragora/Synaptic whatever GUI comes for your package manager. Not like you really need to do this because the average person only cares about the UI applications.
As someone else has said, on distributions that go for ease of use, the terminal isn't really needed.
However, I do consider it a convenience feature even for users who are not savvy with it: You can either troubleshoot an issue by giving instructions like "Open application X, navigate to Option, open Tab, press Button, then enter Text, hit OK and repeat for each" or "copy and paste this command into your terminal". The amount of work on both sides is likely lower plus there's less room for error.
You would have to Give SUSE / OpenSUSE a try. It has Yast2-GUI so everything from setting up a samba share, ftp server, to kernal tweak, system services, and boot setup can be done entirely in the GUI environment. Very similar to how the older Windows Control Panel looked. Also One-click install for rpm files. Oh and system rollback if you blow up the system, no command line fixes needed.