1. You do not need to use sudo to run scripts and binaries, provided they are properly packaged. You just need to make them executable, which any user can do without entering the password.

2. You installed Arch Linux. That is a much more technically demanding accomplishment that simply does not equal to enabling sideloading on an Android device.

3. The official Arch repos do not discriminate on the basis of whether a given package will harm corporate interests, or the interests of the Arch development team. Google Play does - for example, NewPipe, which is a far better YouTube client than the official app in many respects, yet Google bans it for commercial advantage.

In addition with other comments, you are also free to disable this behavior, you are also free to install an alternative "package manager" that will not require a sudo for each package installation ...

And out of the box, you can also install apps in our own user account without needing a sudo.

You also have to use sudo to install from official Arch repos. It would be fine if the Play store required a PIN too.