So you want to install unsigned software that's not even open-source, meaning you're not a developer or anything, you just want something Apple didn't approve. And you want it to be about as easy as installing from the App Store. Sounds fine until every appmaker, realizing most people are capable of installing this way, starts distributing only through those other stores. Then average people have to get everything from there, not the App Store. And all that unapproved software uses whatever tricks they want to.
This doesn't take any imagination; it's already how things work on macOS. Even Chrome isn't on the App Store. But that's on a desktop, so whatever. On a phone, "nobody" needs to mess with this crap, and those who do can use Android.
So instead, Apple tries to lock things down. Yes they're greedy and want the $, but users also like the platform and have the choice in the end, so it's fair. It's an old story. Look at video game consoles for the parallel universe. Nobody forced Nintendo to open the floodgates, and I'm glad for that.